Full custody

What’s the point of getting full custody of your kids?

My baby daddy isn’t involved in our sons lives, he’ll only see them once every 2 weeks when his mom brings them to him. He doesn’t make the effort on his end. He isn’t on their birth certificates. Is there even a point on getting full custody of my boys? I plan on moving with them in Jan or Feb, could he stop that from happening if I don’t have full custody?