Could the father of my unborn baby claim residence in the UK even though he's not from here?

Im just wondering what it would take for a dad to get residence of a newborn?
I'm a pregnant woman have been single since I was about 12 weeks pregnant.
The dad has non stop harassed me and any visitation I ever try and set out for when she is born never seems good enough so I feel when she is born he would probably try to get residence. 
How likely is this to happen and what would happen if he did file for it?
I live in the U.K.
Thank you