What happens when you co-sign for a car and your friend can't make payments?

I know that as a co-signer i am responsible for the car to be paid, but who would own the car if she pays down payment and 1 month and i have pay the last two month cause she can't keep up with it. I think it would be stupid for me if i keep paying and she is driving the car. The car loan is in both of our name but I co-signed for it because she didn't have the credit require, now i would hate to mess my credit up so i am making the payments. What should i do if she doesn't want to give up the car, or give me the car?