I've been in that situation but luckily even having spent only 50 hours on the project we had something written down on day one, basically a '50:50' agreement, signed on paper. Get something written from your future(?) cofounder, especially if he's given up. A couple of years in the future you might have success and he can come back and claim part of it. Like in the movie 'the social network'. Justified or not that would cause trouble and costs regardless the outcome.

Can you purchase his share for a small sum? $100 USD is worth it as long as the other party agrees and gives something in return. And such an offer certainly gets the discussion about ownership and time-spending started.