It's a tough one but I've come to the conclusion that granting the mother custody based solely on the fact that she gave birth to the child is stupid.
Like it or not, while it resides in her womb, she has custody of it.
Way to misread a statement..... FYI, "gave" implies in the past. She already has given birth which means the child is no longer in her womb.
Well then they should work out custody arrangements, but the bloke can't expect to get custody just because he had a one night stand, which seems to be all this 'relationship' amounted to.