UNITED STATES

                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549

                                  SCHEDULE 13G
                    Under the Securities Exchange Act of 1934

                               (Amendment No__)(1)


            AboveNet, Inc. (formerly Metromedia Fiber Network, Inc.)
                     --------------------------------------
                                (Name Of Issuer)

                     Common Stock, par value $0.01 per share

                     --------------------------------------
                         (Title of Class of Securities)

                                    00374N107

                     ---------------------------------------
                                 (CUSIP Number)

                                September 8, 2003

                     ---------------------------------------
             (Date of Event Which Requires Filing of this Statement)

Check the appropriate box to designate the rule pursuant to which this Schedule
is filed:

            [ ]  Rule 13d-1(b)

            [X]  Rule 13d-1(c)

            [ ]  Rule 13d-1(d)

--------

(1) The remainder of this cover page shall be filled out for a
reporting person's initial filing on this form with respect to the subject class
of securities, and for any subsequent amendment containing information which
would alter the disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("the Act") or otherwise subject to the liabilities of that section of the
Act but shall be subject to all other provisions of the Act (however, see the
Notes).

CUSIP NO. 00374N107                     13G

1     NAME OF REPORTING PERSON
      SS. OR IRS IDENTIFICATION NO. OF ABOVE PERSON

            Verizon Communications Inc. #23-2259884
--------------------------------------------------------------------------------
2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                          (A)[ ]
                                                                          (B)[X]
--------------------------------------------------------------------------------
3     SEC USE ONLY

--------------------------------------------------------------------------------
4     CITIZENSHIP OR PLACE OF ORGANIZATION

            Delaware
--------------------------------------------------------------------------------
                            5      SOLE VOTING POWER
        NUMBER OF
         SHARES                          0 (See Item 4)
                            ----------------------------------------------------
                            6      SHARED VOTING POWER
  BENEFICIALLY OWNED BY
                                         436,500 (See Item 4)
                            ----------------------------------------------------
                            7      SOLE DISPOSITIVE POWER
          EACH
        REPORTING                        0 (See Item 4)
                            ----------------------------------------------------
                            8      SHARED DISPOSITIVE POWER
         PERSON
          WITH                           436,500 (See Item 4)

--------------------------------------------------------------------------------

9     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                              436,500 (See Item 4)
--------------------------------------------------------------------------------
10       CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*

                                   See Item 4                                [X]
--------------------------------------------------------------------------------
11       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

                                5.2% (See Item 4)
--------------------------------------------------------------------------------
12       TYPE OF REPORTING PERSON*

                                       HC
--------------------------------------------------------------------------------


                                       2

CUSIP NO. 00374N107                     13G

1     NAME OF REPORTING PERSON
      SS. OR IRS IDENTIFICATION NO. OF ABOVE PERSON

            Verizon Investments Inc. #13-3191789
--------------------------------------------------------------------------------
2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                      (A)[ ]
                                                                      (B)[X]
--------------------------------------------------------------------------------
3     SEC USE ONLY

--------------------------------------------------------------------------------
4     CITIZENSHIP OR PLACE OF ORGANIZATION

            Delaware
--------------------------------------------------------------------------------
                            5      SOLE VOTING POWER
      NUMBER OF
       SHARES                            0 (See Item 4)
                            ----------------------------------------------------
                            6      SHARED VOTING POWER
  BENEFICIALLY OWNED BY
                                         18,200 (See Item 4)
                            ----------------------------------------------------
                            7      SOLE DISPOSITIVE POWER
          EACH
        REPORTING                        0 (See Item 4)
                            ----------------------------------------------------
                            8      SHARED DISPOSITIVE POWER
         PERSON
          WITH                           18,200 (See Item 4)
--------------------------------------------------------------------------------

9     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                               18,200 (See Item 4)
--------------------------------------------------------------------------------

10    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*

                                   See Item 4                                [X]
--------------------------------------------------------------------------------

11    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

                                0.2% (See Item 4)
--------------------------------------------------------------------------------

12    TYPE OF REPORTING PERSON*

                                       HC
--------------------------------------------------------------------------------


                                       3

CUSIP NO. 00374N107                   13G

1     NAME OF REPORTING PERSON
      SS. OR IRS IDENTIFICATION NO. OF ABOVE PERSON

            Verizon Global Networks Inc. #54-1885546

--------------------------------------------------------------------------------
2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                       (A)[ ]
                                                                       (B)[X]
--------------------------------------------------------------------------------
3     SEC USE ONLY

--------------------------------------------------------------------------------
4     CITIZENSHIP OR PLACE OF ORGANIZATION

            Delaware
--------------------------------------------------------------------------------
                            5      SOLE VOTING POWER
        NUMBER OF
          SHARES                         0 (See Item 4)
                            ----------------------------------------------------
       BENEFICIALLY         6      SHARED VOTING POWER
         OWNED BY                        418,300 (See Item 4)
                            ----------------------------------------------------
                            7      SOLE DISPOSITIVE POWER
          EACH
        REPORTING                        0 (See Item 4)
                            ----------------------------------------------------
                            8      SHARED DISPOSITIVE POWER

         PERSON
          WITH                           418,300 (See Item 4)

--------------------------------------------------------------------------------

9     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                              418,300 (See Item 4)
--------------------------------------------------------------------------------
10    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*

                                   See Item 4                                [ ]
--------------------------------------------------------------------------------
11    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

                               5.0% (See Item 4)
--------------------------------------------------------------------------------
12    TYPE OF REPORTING PERSON*

                                       HC
--------------------------------------------------------------------------------

                                       4

Item 1.

      (a)   Name of Issuer

                  AboveNet, Inc. (formerly Metromedia Fiber Network, Inc,)

      (b)   Address of Issuer's Principal Executive Offices

                  360 Hamilton Avenue
                  White Plains, New York  10601

Item 2.

      (a)   Name of Persons Filing

                  Verizon Communications Inc. ("Verizon")
                  Verizon Investments Inc. ("VII")
                  Verizon Global Networks Inc. ("VGNI")
                  Verizon, VII and VGNI collectively may be referred to herein
                  as the "Reporting Persons".

      (b)   Address of Principal Business Office or, if none, Residence

                  Verizon
                  1095 Avenue of the Americas
                  New York, New York 10036

                  VII
                  3900 Washington Street
                  Wilmington, Delaware 19802

                  VGNI
                  1320 N. Court House Road
                  Arlington, Virginia 22201

      (c)   Citizenship

                  Each of Verizon, VII and VGNI is incorporated under the laws
                  of the State of Delaware.



                                       5

      (d)   Title of Class of Securities

                  Common Stock, par value $0.01 per share

      (e)   CUSIP Number

                  00374N107

Item 3. If this statement is filed pursuant to Rule 13d-1(b), or 13d-2(b), check
whether the person filing is a:

(a)   [ ]   Broker or Dealer registered under Section 15 of the Exchange Act

(b)   [ ]   Bank as defined in Section 3(a)(6) of the Exchange Act

(c)   [ ]   Insurance Company as defined in Section 3(a)(19) of the Exchange Act

(d)   [ ]   Investment Company registered under Section 8 of the Investment
            Company Act

(e)   [ ]   Investment Adviser in accordance with Rule 13d-1(b)(1)(ii)(E)

(f)   [ ]   Employee Benefit Plan or Endowment Fund in accordance with 13d-1(b)
            (1)(ii)(F)

(g)   [ ]   Parent Holding Company or Control Person in accordance with Rule
            13d-1(b)(1)(ii)(G)

(h)   [ ]   Savings Association as defined in Section 3(b) of the Federal
            Deposit Insurance Act

(i)   [ ]   Church Plan that is excluded from the definition of an investment
            company under Section 3(c)(14) of the Investment Company Act

(j)   [ ]   Group, in accordance with Rule 13d-1(b)(1)(ii)(J)


Item  4. Ownership

      (a)   Amount Beneficially Owned:

      The Issuer filed a Current Report on Form 8-K with the Securities and
      Exchange Commission ("SEC") on September 8, 2003 in which it reported that
      it had emerged from Chapter 11 of the U.S. Bankruptcy Code on September 8,
      2003 (the "Effective Date"), pursuant to the Issuer's Second Amended Plan
      of Reorganization (the "Plan"). The Reporting Persons believe that they
      may be deemed to have acquired beneficial ownership of in excess of 5% of
      the


                                       6

      Common Stock of the Issuer as of the Effective Date pursuant to the Plan
      in exchange for claims of the Reporting Persons against the Issuer and its
      subsidiaries.

      VII is a direct wholly owned subsidiary of Verizon and may be deemed to be
      the direct beneficial owner of shares of Common Stock of the Issuer. By
      virtue of their relationships, Verizon and VII may be deemed to have
      shared power to vote and dispose of, or to direct the vote and disposition
      of, the shares that may be deemed to be beneficially owned by VII.

      VGNI is a direct wholly owned subsidiary of Verizon and may be deemed to
      be the direct beneficial owner of shares of Common Stock of the Issuer. By
      virtue of their relationships, Verizon and VGNI may be deemed to have
      shared power to vote and dispose of, or to direct the vote and disposition
      of, the shares that may be deemed to be beneficially owned by VGNI.

      The responses of the Reporting Persons to Rows (9) and (10) of the cover
      pages of this Schedule 13G are incorporated herein by reference. VII
      estimates that as of the Effective Date VII may be deemed to beneficially
      own approximately 18,200 shares of Common Stock of the Issuer, which
      includes the right to acquire approximately 8,700 shares of Common Stock
      pursuant to warrants issued by the Issuer to VII pursuant to the Plan. The
      foregoing amount does not include any shares of Common Stock for which VII
      may be able to subscribe pursuant to nontransferable rights issued under
      the Plan and exercisable through the first business day after the 30th day
      after the Effective Date. VGNI estimates that as of the Effective Date
      VGNI may be deemed to beneficially own approximately 418,300 shares of
      Common Stock of the Issuer.

      As of the date hereof, the Reporting Persons have been only able to
      estimate the number of shares of Common Stock they may be deemed to
      beneficially own because the Reporting Persons have not yet received
      information sufficient to determine with precision the number of shares of
      Common Stock received or receivable pursuant to the Plan. Such number of
      shares cannot be finally determined until the actual amount of Allowed
      Claims (as defined in the Plan) has been finally determined by the Issuer.

      (b) Percent of Class:

      The responses of the Reporting Persons to Row (11) of the cover pages of
      this Schedule 13G are incorporated herein by reference. For purposes of
      calculating the percent of Common Stock that may be deemed to be
      beneficially owned, the Reporting Persons estimate that there were
      approximately 8,306,465 shares of Common Stock outstanding as of the
      Effective Date, based on information set forth in the Plan and in the
      Issuer's Form 8-K filed with the SEC on September 8, 2003. For purposes of
      such calculation for Verizon and VII, an additional 8,700 shares of Common
      Stock that VII has the right to acquire pursuant to warrants


                                       7

      that may be deemed to be beneficially owned by it, are to be deemed
      outstanding, in accordance with Rule 13d-3 under the Exchange Act.

      As of the date hereof, the Reporting Persons have been only able to
      estimate their percent of class that may be deemed to be beneficially
      owned because the Reporting Persons have not yet received information
      sufficient to determine with precision (i) the number of shares of Common
      Stock received or receivable pursuant to the Plan and (ii) the number of
      shares of Common Stock outstanding. Such numbers of shares cannot be
      finally determined until the actual amount of Allowed Claims (as defined
      in the Plan) has been finally determined by the Issuer.

      (c)   Number of shares as to which such person has:

            (i) sole power to vote or to direct the vote, (ii) shared power to
            vote or to direct the vote, (iii) sole power to dispose or to direct
            the disposition, and (iv) shared power to dispose or to direct the
            disposition, in each case are incorporated by reference from the
            responses of the Reporting Persons to Rows (5) through (8) of the
            cover pages of this Schedule 13G and Item 4(a) hereof.

Item 5. Ownership of Five Percent or Less of a Class:

      Not Applicable

Item 6. Ownership of More Than Five Percent on Behalf of Another Person:

      Not Applicable.

Item 7. Identification and Classification of the Subsidiary Which Acquired the
Security Being Reported On by the Parent Holding Company:

      See Item 4.

Item 8. Identification and Classification of Members of the Group:

      Not Applicable.

Item 9. Notice of Dissolution of Group:

      Not Applicable.

Item 10. Certifications:

(b) By signing below I certify that, to the best of my knowledge and belief, the
securities referred to above were not acquired and are not held for the purpose
of or


                                       8

with the effect of changing or influencing the control of the issuer of the
securities and were not acquired and are not held in connection with or as a
participant in any transaction having that purpose or effect.



                                       9

                                   SIGNATURES

         After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete and
correct.

                                      September 17, 2003
                                      ------------------------------------------

                                      VERIZON COMMUNICATIONS INC.

                                      /s/Marianne Drost
                                      ------------------------------------------
                                               Signature

                                      Marianne Drost -
                                      Senior Vice President, Deputy General
                                      Counsel and Corporate Secretary
                                      ------------------------------------------
                                               Name/Title

                                      VERIZON INVESTMENTS INC.

                                      /s/Janet M. Garrity
                                      ------------------------------------------
                                               Signature

                                      Janet M. Garrity - President and Treasurer
                                      ------------------------------------------
                                               Name/Title

                                      VERIZON GLOBAL NETWORKS INC.

                                      /s/Robert S. Fitzmire
                                      ------------------------------------------
                                               Signature

                                      Robert S. Fitzmire - Treasurer
                                      ------------------------------------------
                                               Name/Title



                                       10

                                                                       EXHIBIT A

                         AGREEMENT AS TO JOINT FILING OF

                                  SCHEDULE 13G

         The undersigned hereby agree and consent to the joint filing on their
behalf of this Schedule 13G.

                                   September 17, 2003
                                   ---------------------------------------------

                                   VERIZON COMMUNICATIONS INC.

                                   /s/Marianne Drost
                                   ---------------------------------------------
                                            Signature

                                   Marianne Drost -
                                   Senior Vice President, Deputy General
                                   Counsel and Corporate Secretary
                                   ---------------------------------------------
                                            Name/Title

                                   VERIZON INVESTMENTS INC.

                                   /s/Janet M. Garrity
                                   ---------------------------------------------
                                            Signature

                                   Janet M. Garrity - President and Treasurer
                                   ---------------------------------------------
                                            Name/Title

                                   VERIZON GLOBAL NETWORKS INC.

                                   /s/Robert S. Fitzmire
                                   ---------------------------------------------
                                            Signature

                                   Robert S. Fitzmire - Treasurer
                                   ---------------------------------------------
                                            Name/Title





                                       11