Ex wants to move away with the kids

I've recently broken up with my boyfriend of 18yrs as he was cheating. He moved to where I live, we met and had three kids together. I think 50-50 custody is best for the kids and for us. My ex is saying that he's moving back to where he used to live and taking the kids with him as he has just as much rights as I do. I would never dream of moving the kids away from their dad. The kids were all born here and grew up here, have schools, friends ect. This is their home. What do I do?