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Business & farm
I would emphasize @rjs 's point that you need to get a professional appraisal of the home's fair market value at the time of the buyout. The actual net worth of the home will then be its fair market value less the remaining mortgage balance. Each co-owner's share would be 50% of that amount (assuming that all ownership costs have been split 50/50 prior to the buyout.)
Let's say that the home's net worth after this calculation is $1 million. That would make each co-owner's fair share $500K. If your co-owner sells you his $500K share for $200K, then he's given you a gift of $300K. That's how the gift tax issue could come into the picture.
Your cost basis would be a different calculation. Mortgage balances are not part of the cost basis calculation.