If an Aura is put onto the battlefield without being cast, the Aura's controller-to-be chooses what it will enchant as it comes back onto the battlefield. An Aura put onto the battlefield this way doesn't target anything (so it could be attached to an opponent's permanent with hexproof, for example), but the Aura's enchant ability restricts what it can be attached to. If the Aura can't legally be attached to anything, it remains in its current zone.

If an Aura is being put onto the battlefield at the same time as a creature, that Aura can't enchant that creature.