hel vårdnad?

Hi....

I have a dilemma.....I recently had a baby...I registered him under the name of me and his father.
The problem is that I want to have the complete vårnad as we are not married and he lives in Norway.
I am mammaledigt now in 100 porcentage....only me.
Now the father....(with whom I do not have a good relationtionship ) wants to enjoy of the pappaledighet in Norway and asks for papers or documents to do so.

Does this affects me in any way? I mean if he registeres the baby in norway....does it mean that he also have the vårnad?