If you put the father's name on the birth certificate he will automatically have parental responsibility, which means he has a lot of rights over the child.
If you don't, he will have to apply to the courts for it. Without the court giving him parental responsibility he will have no rights over the child at all.
It is never cut and dried - the courts will always do the best for the child, not the parents, 'acting in the best interests of the child'.
The courts would probably make different decisions for a new born baby and a ten year old who had been brought up in the same house as his father.
Sorry there is no straightforward, simple answer.