When Thopter Arrest enters the battlefield, exile target artifact or creature an opponent controls until Thopter Arrest leaves the battlefield.
The exiled card returns to the battlefield immediately after Thopter Arrest leaves the battlefield. Nothing happens between the two events, including state-based actions.
In a multiplayer game, if Thopter Arrestâ€™s owner leaves the game, the exiled card will return to the battlefield. Because the one-shot effect that returns the card isnâ€™t an ability that goes on the stack, it wonâ€™t cease to exist along with the leaving playerâ€™s spells and abilities on the stack.
If Thopter Arrest leaves the battlefield before its triggered ability resolves, the target permanent wonâ€™t be exiled.
If a token is exiled this way, it will cease to exist and wonâ€™t return to the battlefield.
Auras attached to the exiled permanent will be put into their ownersâ€™ graveyards. Any Equipment will become unattached and remain on the battlefield. Any counters on the exiled permanent will cease to exist.