#triggered abilites

When Necromancy enters the battlefield, its ETB effect will trigger and Yarok will cause it to trigger an additional time. Each trigger can target a different creature card in a graveyard and each trigger will return its target to the battlefield under your control. Necromancy will end up as an aura attached to the target of the trigger that resolved last, but the first creature will be just fine without Necromancy attached to it, so long as Necromancy is still on the battlefield. When Necromancy leaves the battlefield, both of the creatures it returned to the battlefield will be sacrificed, if any of the are still on the battlefield.

You lose here.

Transcendence’s “lose the game” trigger is what’s known as a state trigger. State triggers are a special type of triggered ability. Rather that triggering when something specific happens (e.g. “whenever you draw a card”), state triggers trigger when a specific condition is met in the game (e.g. “when you have 20 or more life”). 

Because the state that triggers a state trigger is likely to continue, state triggers have a special rule that keep them from triggering endlessly. If there wasn’t this special rule, then the state trigger would trigger. Then it would trigger again. And again. And again. And again. And the game would be frozen and unable to continue. So instead of that happening, a state trigger can’t trigger again as long as that trigger is already on the stack. When the trigger leaves the stack, the state trigger will trigger again if the state is still true (and the source of the trigger is still around to trigger.)

What this means for the scenario you describe is the following:

Transcendence is cast. It resolves and enters the battlefield under your control. Its “lose the game” trigger triggers because you have 20+ life and goes on the stack. It doesn’t trigger again since there’s already a copy of the trigger on the stack.

Before the trigger resolves, you use Zedruu’s activated ability to give control of Transcendence to your opponent.

Your opponent has 20+ life as well, so Transcendence would trigger except that there’s still a copy of its trigger on the stack. The copy that you control. Even though Transcendence has a new controller, it’s still the same object that created that trigger and so its state trigger won’t trigger again until that copy of the trigger is no longer on the stack.

Transcendence’s trigger resolves and you lose the game. All cards you own leave the game with you, so Transcendence is no longer on the battlefield once the trigger has resolved and thus its state trigger won’t trigger for your opponent.

Yes, but a slow one.