Aminatou, the Fateshifter

As Aminatou's third ability resolves, you choose a direction, then each player takes control of their new permanents at the same time.

You draw a card and put one back all while Aminatou's first ability is resolving. Nothing can happen between the two, and no player may choose to take actions.

Once the exiled permanent returns, it's considered a new object with no relation to the object that it was. Auras attached to the exiled permanent will be put into their owners' graveyards. Equipment attached to the exiled permanent will become unattached and remain on the battlefield. Any counters on the exiled permanent will cease to exist.

Aminatou's second ability can target any permanent you own, including those another player controls.