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When two or more owners each have a partial interest in a property each of the owners is responsible for the tax on their own gain.
If one of the owners buys out the other then the one that is selling has to compute the gain or loss on the buyout. For example, if the cost was 20K and that owner id bought out for 30K then there is a 10K gain. The buyer of that interest for 30K would add that 30K cost to their intital cost and use the total cost to figure their gain on a later sale.
For family members and related parties additional rules reqire that the sale be at fair market value so that a brother could not claim a loss or avoid tax on their part of the gain by the sister selling at less than the value.
I hope this helps to know that each owner must pay the tax on their portion, if any, and the one that buys out another adds that cost to use as part of their basis to figure gain.