Think about it, don't give him parental responsibility and be able to do what you believe is best for your child, then if he decides to pull himself together and be a good father it's as simple as you both signing a piece of paper to grant him it.
Or do give him it, realise he is actually an arse (that urinates in bedrooms!), move on and for some reason or other wish to give a new partner PR. eg. I am pg now, could have problems and end up in hospital, dp needs to be able to take resp. for my two but he can't legally because to grant him PR we have to take it to court and get XDP's PR taken away, or get him to agree to DP having PR, or prove to a judge that it is in my childs best interests.
Long-winded and avoidable.
With DD he doesn't even have to know, but the second I take him to court WRT DS he knows he has equal say in his schooling, where he lives, if she leaves the country to go on holiday, if he ever goes to the docs/hospital for something etc etc etc.
Unless you are sure you want to give the father 100% control over yours and your childs life, do not put him on the birth certificate.