If you are conceiving with a known donor or co-parent, it is important to consider what legal status your child's biological father will have, and whether you need to take any steps to manage your situation. The law is complicated, and depends on your status as well as your donor's.
If you are married or in a civil partnership and conceive by artificial insemination, then you are entitled to put both your names on the birth certificate and would be the legal parents. This does not mean that the sperm donor could not make a claim to the court for contact. Each case would be considered on an individual basis, with the best interests of the child being paramount.
It is important to get a legal donor agreement in place to help prevent future disputes.