Sergiy (12/16/2008)

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Just don't update what does not need to be updated:

 update [my_table]
         set [row_uid] = newid()
         from [deleted] A
         where A.[UID]=my_table.[UID]
             and my_table.[row_uid] IS NULL

bitbucket (12/16/2008)

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What is your value for "nested triggers" option (ON or OFF)

Are they any other triggers on this table which update the table?

You might want to check BOL (Nested triggers) for SQL 2000 at:

http://msdn.microsoft.com/en-us/library/aa214644(SQL.80).aspx