Hilchos Bikkurim 9:11

Let’s say that a kohein and a Yisroel are negotiating joint ownership of an animal. If the kohein makes a condition that the partnership doesn’t include the gifts, then the gifts belong to the kohein. Since the kohein excluded them, he left himself the part of the animal that includes the gifts, making them his. However, if he told the Yisroel that the partneship is on condition that the kohein owns the gifts, the gifts belong to the Yisroel and he can give them to any kohein he likes. Even though the kohein made a condition that they were his, the animal is not exempted from having to give the gifts from it. This is because his condition didn’t give him ownership of the gifts. Since he doesn’t have a share in them, his condition doesn’t acquire them.

Hilchos Bikkurim 9:12

If a kohein jointly owns an animal’s head, he need not give the jaw. If he jointly owns the animal’s front leg, he need not give the foreleg. If he jointly owns the animal’s innards, he need not give the abomasum. If the kohein tells the Yisroel, “The whole animal is mine, but the head is yours,” then the jaw must be given because the part that is obligated in the gifts belongs to the Yisroel.