Do fathers have 50/50 rights as the mother ?

I was told by Social Services last month as I was trying to help a friend out when he split with his babies mother. They said that because he is on the birth certificate then he does have as much rights as the mother. But if the father does was full custody then the mother does have to agree to it otherwise it will be down to the solicitors. But during this time the baby can stay with the father or the mother.