Marchesa, la Rose Noire

Dethrone doesn't trigger if the creature attacks a planeswalker, even if its controller has the most life. The same is true if the creature attacks a battle, even if its protector has the most life.

If a creature has multiple instances of dethrone, each triggers separately.

If the creature card leaves the graveyard before the delayed triggered ability resolves, that card won't return to the battlefield, even if it's back in the graveyard when the delayed triggered ability resolves.

If Marchesa has a +1/+1 counter on it when it dies, it will return to the battlefield under your control because of its own ability.

The +1/+1 counter is put on the creature before blockers are declared.

In a Two-Headed Giant game, dethrone will trigger if the creature attacks either player on the team with the most life or tied for the most life.

Once dethrone triggers, it doesn't matter what happens to the players' life totals before the ability resolves. You'll put a +1/+1 counter on the creature even if the defending player doesn't have the most life as the ability resolves.