Once Scrambleverse starts to resolve, no player may respond until it has finished resolving. For example, you can’t wait to see who will control a creature before deciding whether or not to activate one of its abilities.

For each nonland permanent, any player may be randomly chosen, including the permanent’s current controller.

All of the control-change effects happen at the same time.

Each nonland permanent will untap, no matter which player was randomly chosen to gain control of it.