I've had an ally betray me on the battlefield once or twice. It has been awhile so I don't recall specifics. Since that happened I have been cautious to always leave some units facing my ally so that he doesn't get any bright ideas. You have to watch carefully, because the AI will hide behind your melee units while you take on a tough enemy army. I do a lot of:
"You first."
"No, be my guest."
"Oh no, I must insist that you have the honor of engaging the enemy first in glorious battle."
This little dance is the key to holding provinces after a battle... Fortunately the AI usually ends up engaging first because it will send cav or skirmishers forward piecemeal.

As has been said, the winning allied army with the most men at the end of the battle is the one that gets posession. The AI is very opportunistic about this. If you build up to take a province that you both border, it will throw in a huge army so that it gets control in the end (or if the enemy fails to take the field.) I've learned to throw in everything I can muster to prevent the AI from "free loading" off of my attacks.