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                                                                   EXHIBIT 10.35

                              SECOND AMENDMENT TO
                             TAX SHARING AGREEMENT


     This Second Amendment to the Tax Sharing Agreement dated as of December 3,
1996, by and among Tele-Communications, Inc., a Delaware corporation ("TCI"),
Liberty Media Corporation, a Delaware corporation ("Liberty"), Tele-
Communications International, Inc. ("International"), TCI Technology Ventures,
Inc. ("Technology"), TCI Communications, Inc. ("TCIC"), TCI Cable Investments,
Inc. ("TCICI"), TCI Starz, Inc. ("Starz") and TCI CT Holdings, Inc. ("CT").

                              W I T N E S S E T H:
                              - - - - - - - - - - 

     WHEREAS, the parties have entered into a Tax Sharing Agreement (the
"Agreement") effective July 1, 1995, as amended by the First Amendment to Tax
Sharing Agreement, dated as of October 1995; and

     WHEREAS, the parties now wish to amend the Agreement to provide for the
treatment of indirect subsidiaries of TCI that become direct, first-tier
subsidiaries of TCI;

     NOW, THEREFORE, the parties hereby agree as follows:

     1.  Section A of the Agreement is amended by adding thereto the following
new definitions:

          "CT" means TCI CT Holdings, Inc.
           --                             

          "First-Tier Subsidiary" means any subsidiary of TCI that would qualify
           ---------------------                                                
     as a member of the TCI Group based solely on the stock of such subsidiary
     owned directly by TCI.

          "Membership Date" means, for any member of the TCI Group, the date
           ---------------                                                  
     that such entity became, and since which has continuously remained, a
     member of the TCI Group.

          "Starz" means TCI Starz, Inc.
           -----                      

     2.   The definition of "Subgroup Parent" is amended to read as follows:

          "Subgroup Parent" means each of Liberty, International, Technology,
           ---------------                                                   
     TCIC, TCICI, Starz, CT and any other First-Tier Subsidiary formed or
     acquired after the date hereof.
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     3.   Section H.6. of the Agreement is amended by adding thereto the
following at the end thereof:

          "If to a member of the Subgroup of any other Subgroup Parent, to such
     Subgroup Parent at its address as shown in the books and records of TCI."

     4.   The Agreement is amended by adding thereto a new Section I, as
follows:

          "I.  Promotion of Subsidiaries.
               ------------------------- 

           1.  Raised Subsidiaries.  Anything contained herein to the contrary
               -------------------                                            
     notwithstanding, if any Subgroup Member (a "Raised Subsidiary") becomes a
     First-Tier Subsidiary (as a result of any spin-off, dividend, distribution,
     liquidation, merger, transfer or other transaction, or any series of any
     such transactions, whether or not related), other than in connection with
     any transaction or series of related transactions in which such Subgroup
     Member subsequently ceases to be a First-Tier Subsidiary but remains a
     member of the TCI Group, then from and after the time (the "Promotion
     Time") that such Raised Subsidiary so becomes a First-Tier Subsidiary:

               a.  such Raised Subsidiary shall be deemed to have been a
          Subgroup Parent (and such Raised Subsidiary and its Subsidiaries at
          the Promotion Time shall be deemed not to have been Subsidiaries of
          any other Subgroup), for all purposes of this Agreement, from the
          later of (i) the Effective Date, and (ii) the Membership Date with
          respect to such Raised Subsidiary (and for purposes of Section C.4. of
          this Agreement, from the later of (i) January 1, 1995, and (ii) such
          Membership Date);

               b.  TCI shall establish and maintain an Intercompany Account
          between it and such Raised Subsidiary, which shall be credited with
          any Tax Benefits and charged with any Tax Liabilities attributable to
          the Subgroup of such Raised Subsidiary or any Subgroup Member thereof,
          as provided in Section B.1. of this Agreement, determined on a
          retroactive basis from the Effective Date; and

               c.  the Intercompany Account of each Subgroup of which the Raised
          Subsidiary or any of its Subsidiaries at the Promotion Time was a
          member, at any time prior to the Promotion Time, shall be
          appropriately adjusted to reflect the effect of clause a. of this
          Section I.1. on a retroactive basis from the Effective Date.

           2.  General Rule.  Except as otherwise expressly provided in Section
               ------------                                                    
     I.1. of this Agreement, the provisions of this Agreement shall apply to any
     Raised Subsidiary with the same effect as to any other Subgroup Parent.


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           3. Execution.  For the avoidance of doubt, each Raised Subsidiary
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     shall automatically become a party to this Agreement, effective as of the
     Promotion Time relating thereto, and shall execute and deliver a
     counterpart of this Agreement to evidence the same, as soon as practicable
     following such Promotion Time."

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


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     IN WITNESS WHEREOF, the parties have executed this Amendment effective as
of the Effective Date (as defined in the Agreement).

TELE-COMMUNICATIONS, INC.                   TCI TECHNOLOGY VENTURES, INC. 
                                                                          
By /s/ Stephen M. Brett                     By /s/ David Boileau          
   --------------------------               ------------------------------
                                                                          
                                                                          
LIBERTY MEDIA CORPORATION                   TCI STARZ, INC.               
                                                                          
By /s/ Robert R. Bennett                    By /s/ Stephen M. Brett       
   --------------------------               ------------------------------
                                                                          

TELE-COMMUNICATIONS INTERNATIONAL, INC.     TCI CT HOLDINGS, INC.         
                                                                          
By /s/ Graham Hollis                        By /s/ Stephen M. Brett        
   --------------------------               ------------------------------


TCI COMMUNICATIONS, INC.

By /s/ Barney Schotters
   ---------------------------


TCI CABLE INVESTMENTS, INC.

By /s/ Barney Schotters
   ---------------------------


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