The owner of the permanent chooses where the card ends up. All players get to know that choice.

In some unusual cases—though getting less unusual all the time—a permanent will be comprised of multiple cards, such as a melded permanent or a mutated creature. In those cases, the owner of the permanent puts all those cards second from the top (that is, just under the top card) or on the bottom in any order. Other players get to know which one they chose, but they don't get to know the relative order of the cards.