Basis determination

Question

Say A & B buy a property. Each pays P1, which then is each one's basis. Later, B sells to A for P2. For B, the gain would be P2 - P1. Is it correct, that A now holds 2 'assets', one with a basis of P1, the other with a basis of P2?

Would that change if B died, rather than selling, and A inherited B's share? (Presuming an assessment determined the value of B's share to be P2 when they died.)

Answer 1

B originally had an undivided half interest in the property, for which he paid P1; that's his basis. After the transaction he is the sole owner entire property, for which he paid a total of P1 + P2; that's his basis.