My partner rather stupidly had an affair. Now the other woman is claiming to be pregnant with his child. This could or could not be true. (we live in the UK).

Due to constant harassment by anonymous phone calls, emails claiming to be from someone else, and threats from this woman to myself (she thinks my partner and I are not together, but is trying to find out), I have had to get the police involved.

My question (obviosuly firstly we need to establish if he is the father), is that neither of us wants her to bring up the child if he is the father, as she is mentally unstable, we don't see her as being a fit mother, and we both fear for the child's future. She already has two children through fertility treatment when with her husband (now separated). Trying to deal with her if she does keep the child would be absolute hell. Can my partner, and how do he fight for custody of the baby from birth?

He get's a solicitor and files for full custody in court.