The owner of a card in Magic refers to the player who started the game with this card in his or her deck. There are multiple ways for cards and permanents to change controllers, but the owner of card always remains the same. Cards can only be put into the hand, graveyard and library of their owner, and never into those zones that are controlled by other players. If an effect attempts to put a card into the zone of another player, then the card will go to the appropriate zone of its owner instead.

In most cases the cards themselves make this clear and refer to putting cards into the zones controlled by their owner. For example, Banishment Decree instructs its controller to put the targeted artifact, creature or enchantment on top of its owner’s library. Sometimes cards have received errata to make this even more clear. As mentioned above, cards can only go to the library of their owner, but Elixir of Immortality received slight errata to make it even more clear that the Elixir itself goes to the library of its owner. Elixir of Immortality’s official Oracle text instructs you to “Shuffle Elixir of Immortality and your graveyard into their owner’s library.”