What happens in the battle between Poseidon vs. Hades vs. Zeus?

There was never a battle between them, atleast not formally. Each of the three brother worked together to banish the titans, when it was all over with, they each picked a haven, zeus recieved the upper world, poseiden the water, and hades became king of the underworld, however he wasn't happy with this domain and there are stories of him constantly trying to take zeus's throne.