Zedruu

[Thefluffymacheen]

So if you were to play an enchantment, such as  {Oblivion Ring}, and then give an opponent control of it with  {Zedruu the Greathearted}, would it switch to their battlefield?

[Piotr]

{Oblivion Ring} would switch to the opponent's battlefield but the exiled creature would still be in exile.

[Co2]

The battlefield is only one zone that exists for both player. Unlike a graveyard, there's two graveyard and one battlefield. So it doesn't leave/enter the battlefield again