Yosef Karo

“ And if a kosher animal is found, the Yisrael takes it, and he is exempt from the gifts (Mordechai, quoting from Rabeinu Yitzchak) .
26 In what situations are these words applicable? When the Kohein and the non-Jew are partners in the animal. They are exempt as partners in all of it, even in the smallest part. But if the Kohein and the non-Jew are partners only in the head, the Yisrael is exempt only from the cheek. If the Kohein and the non-Jew are partners with him in the hand, he is exempt only from the arm. And if he is a partner with them in the stomach, he is exempt only from the liver. ”

“ But when a firstborn had one that's equal to it given to the Kohen but it got sold to an Yisrael and mixed among other beasts - if there are many that shekht them they are all exempt, as each one can say "Mine is the firstborn" - but if one person shekhts all of them they only exempt him for one of them.
21 Gifts are applicable anywhere, whether in the Land or outside of it, whether in the presence of the Temple or not. There are those that say the gifts are not applicable outside the Land, and that's their practice.
22 Kohanim are exempt from giving the gifts. ”