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                                                                   EXHIBIT 10.12




                               EIGHTH AMENDMENT TO

                              TAX SHARING AGREEMENT

                                  BY AND AMONG

                                   AT&T CORP.,

                           LIBERTY MEDIA CORPORATION,
                FOR ITSELF AND EACH MEMBER OF THE LIBERTY GROUP,

                               AT&T BROADBAND LLC,

                           LIBERTY VENTURES GROUP LLC,

                            LIBERTY MEDIA GROUP LLC,

                                TCI STARZ, INC.,

                             TCI CT HOLDINGS, INC.,

                                       AND

            EACH COVERED ENTITY LISTED ON THE SIGNATURE PAGES HEREOF,




                            DATED AS OF JULY 25, 2000



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                  This Eighth Amendment, dated as of July 25, 2000 (this "Eighth
Amendment"), to the Tax Sharing Agreement (the "Agreement") dated as of March 9,
1999, as amended by the First Amendment to the Tax Sharing Agreement dated as of
May 28, 1999, the Second Amendment (the "Second Amendment") to the Tax Sharing
Agreement dated as of September 24, 1999, the Third Amendment to the Tax Sharing
Agreement dated as of October 20, 1999, the Fourth Amendment to the Tax Sharing
Agreement dated as of October 28, 1999, the Fifth Amendment to the Tax Sharing
Agreement dated as of December 6, 1999, the Sixth Amendment to the Tax Sharing
Agreement dated as of December 10, 1999, and the Seventh Amendment to the Tax
Sharing Agreement dated as of December 30, 1999, is entered into by and among
AT&T Corp., a New York corporation ("AT&T"), Liberty Media Corporation, a
Delaware corporation ("Liberty"), for itself and on behalf of each member of the
Liberty Group, AT&T Broadband LLC (f.k.a. Tele-Communications, Inc.), a Delaware
limited liability company, Liberty Ventures Group LLC, a Delaware limited
liability company, Liberty Media Group LLC, a Delaware limited liability
company, TCI Starz, Inc., a Colorado corporation, TCI CT Holdings, Inc., a
Delaware corporation, each Covered Entity listed on the signature pages hereof,
and each entity which becomes a party to the Agreement pursuant to Section 23
thereto. Unless otherwise stated herein, capitalized terms used in this Eighth
Amendment shall have the meaning ascribed to such terms in the Agreement.

                  WHEREAS, the parties have entered into the Agreement which
governs the sharing, allocation and reimbursement of federal, state, local and
foreign taxes by the members of the Common Stock Group and the Liberty Group;

                  WHEREAS, AT&T intends to acquire Video Services Corporation, a
Delaware corporation ("VSC"), pursuant to an Agreement and Plan of Merger dated
as of July 25, 2000 (the "VSC Merger Agreement") for and on behalf of the
Liberty Group;

                  WHEREAS, the parties intend that any Tax Items arising from or
relating to the VSC Merger (as defined below), including any Tax Items of VSC or
any of its direct or indirect assets or subsidiaries, shall be considered Tax
Items attributable to the Liberty Group except to the extent set forth herein;
and

                  WHEREAS, the parties now wish to amend the Agreement in
certain respects to clarify the intent of the parties with respect to the
sharing, allocation and reimbursement of federal, state, local and foreign taxes
by the members of the Common Stock Group and the Liberty Group and to make such
other amendments, as provided herein;

                  NOW, THEREFORE, in consideration of the mutual covenants
contained herein, the parties hereby amend the Tax Sharing Agreement as follows:


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                  1. The Agreement is amended by inserting as Section
3(d)(xvii):

                  "(xvii) VSC Merger. Any Tax Item arising from or relating to
VSC, E-Group Merger Corp. ("VSC Merger Sub") or any of their respective direct
or indirect subsidiaries or affiliates (or any predecessor or successor of any
of the foregoing under applicable corporate, limited liability company,
partnership or other organizational law) (the "VSC Entities"); the status of any
member of the Common Stock Group as the successor under Code Section 381 (or
comparable provision of state, local or foreign Tax law) to any of the VSC
Entities; any direct or indirect asset, liability, business, investment or
operation of any of the VSC Entities; the merger of VSC Merger Sub with and into
VSC (the "VSC Merger"), the VSC Merger Agreement, the Employment Agreements (as
defined in the VSC Merger Agreement), the Exchange Agent Agreement (as defined
in the VSC Merger Agreement), the Rule 145 Agreement (as defined in the VSC
Merger Agreement), the Voting Agreement (as defined in the VSC Merger
Agreement), the Company Transaction Documents (as defined in the VSC Merger
Agreement), the Post-Merger Restructuring Transactions (as defined in the VSC
Merger Agreement), the issuance of New Liberty Media Group Tracking Stock in the
VSC Merger or any other transaction contemplated by the VSC Merger Agreement,
the Seventh Supplement to Inter-Group Agreement dated July 25, 2000 (the
"Seventh Supplement"), or this Eighth Amendment, or any other document to which
VSC, Liberty or any of their respective Subsidiaries (as defined in the VSC
Merger Agreement) or Affiliates (as defined in the VSC Merger Agreement) is a
party that is referred to in the VSC Merger Agreement, the Seventh Supplement,
the Employment Agreements (as defined in the VSC Merger Agreement), the Exchange
Agent Agreement (as defined in the VSC Merger Agreement), the Rule 145 Agreement
(as defined in the VSC Merger Agreement), the Voting Agreement (as defined in
the VSC Merger Agreement), the Company Transaction Documents (as defined in the
VSC Merger Agreement), or this Eighth Amendment or executed in connection
therewith (any of the foregoing Tax Items specified in this sentence shall be
referred to hereinafter as a "VSC Tax Item"), shall be for the account of the
Liberty Group (except to the extent otherwise provided in this Section
3(d)(xvii) with respect to any VSC Tax Item), and Liberty shall pay AT&T any Tax
(or any reduction in any Tax refund, credit or other benefit) attributable
thereto. Notwithstanding anything in the preceding sentence to the contrary, any
VSC Tax Item shall be for the account of AT&T hereunder if, and to the extent
that, (x) such VSC Tax Item arises directly from and would not have arisen but
for (i) any breach by AT&T or VSC Merger Sub of any of their representations or
covenants in Sections 2.6 and 5.4 of the VSC Merger Agreement, (ii) any breach
by AT&T of any representation or covenant in the Inter-Group Agreement (except
in the case of clauses (i) and (ii), to the extent arising out of or relating to
the adoption by the Capital Stock Committee of the AT&T Board of Directors of
the resolutions attached as Exhibit A to the Second Supplement or any action
taken by AT&T or any other member of the Common Stock Group in good faith in
accordance with the terms of the Second Supplement or Second Amendment in
connection with the Stock Repurchase Program (as defined in the Second
Supplement) or any Repurchase Transaction or actions taken by AT&T at the
request of Liberty as contemplated by Section 1.2(d) of the Seventh Supplement
or otherwise in writing) or (y) such VSC Tax Item arises from or relates to the
ownership by any member of the Common Stock Group of any stock of, or any
interest in, VSC that is held for the

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account of the Common Stock Group, and AT&T shall pay to the applicable
Governmental Authority or to Liberty any Tax, and shall pay to Liberty any
reduction in any Tax refund, credit or other benefit that is for the account of
Liberty hereunder, attributable thereto."

                  2. The Agreement is amended by (i) deleting in Section 9(b)
the word "or" after the words "or any Subsidiary of Todd during any such period
for such period," and before the words "(VI) Soundelux for any taxable period
 . . ." and (ii) inserting in Section 9(b) the words ", or (VII) VSC for any
taxable period ending on or prior to the date of the closing of the VSC Merger
or any Subsidiary of VSC during any such period for such period" after the words
"or any Subsidiary of Soundelux during any such period for such period" and
before the words "; provided, however, that (i) AT&T shall be entitled to
participate . . . ."

                  3. The Agreement is amended by (i) inserting in Section
3(d)(xiv) the words "VSC Merger Sub," after the words "Soundelux Merger Sub,"
and before the words "nor 4MC Merger Sub . . ."; (ii) inserting in Section
3(d)(xiv) the words "VSC Merger Agreement," after the words "Soundelux Merger
Agreement," and before the words "or 4MC Merger Agreement . . ."; and (iii)
inserting in Section 3(d)(xiv) the word "VSC," after the words "any action (or
failure to act) of any of AGI, Ascent, Todd, Soundelux," and before the words
"4MC or any of their respective subsidiaries. . . ."

                  4. Except as otherwise expressly provided herein, the
Agreement shall continue in full force and effect without modification.






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                  IN WITNESS WHEREOF, each of the parties has caused this Eighth
Amendment to be executed by its respective duly authorized officer as of the
date first set forth above.



                                     AT&T CORP.


                                     By: /s/
                                        ----------------------------------------
                                     Name:
                                     Title:




                                     LIBERTY MEDIA CORPORATION, for
                                     itself and for each member of the Liberty
                                     Group


                                     By: /s/
                                        ----------------------------------------
                                     Name:
                                     Title:






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Each of the Covered Entities listed below on this page hereby executes this
Eighth Amendment as a member of the Liberty Group to acknowledge that such
Person is bound by this Eighth Amendment as a member of the Liberty Group:


                                     LIBERTY SP, INC.


                                     By: /s/
                                         ---------------------------------------
                                     Name:
                                     Title:


                                     LIBERTY AGI, INC.


                                     By: /s/
                                         ---------------------------------------
                                     Name:
                                     Title:


                                     LMC INTERACTIVE, INC.


                                     By: /s/
                                         ---------------------------------------
                                     Name:
                                     Title:




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                                     AT&T BROADBAND LLC


                                     By: /s/
                                         ---------------------------------------
                                     Name:
                                     Title:


                                     LIBERTY VENTURES GROUP LLC

                                     By: /s/
                                         ---------------------------------------
                                     Name:
                                     Title:


                                     LIBERTY MEDIA GROUP LLC

                                     By: /s/
                                         ---------------------------------------
                                     Name:
                                     Title:


                                     TCI STARZ, INC.


                                     By: /s/
                                         ---------------------------------------
                                     Name:
                                     Title:


                                     TCI CT HOLDINGS, INC.


                                     By: /s/
                                         ---------------------------------------
                                     Name:
                                     Title: