She already has sole legal custody as an unmarried mother. He can petition for visitation and pay child support.
Not without the permission of the child's biological mother. When a couple are not married and there is not a custodial order from the court, the law presumes that the mother has sole custody of the child in question.
mother has sole custody even if living with father
The mother. The father have to petition the court for custody or visitation right.
If married, both parents. If single, the mother
If the parents have never married and live separately with their own parents, a court would need to decide on custody. Typically, the court will place the child with the mother, but the best interests of the child are primary.
The mother is presumed to have custody unless there is a court order saying otherwise.
the person who has physical possesion of the child.
The mother. If she dies, her parents get custody.
When married you have equal rights to the child.
Depends on circumstances. A single mother has a presumption of sole custody at the time of the birth of the child. Where married parents are separated, there is a presumption of joint physical custody whether or not support is ordered.
When the parents aren't married the mother has sole custody of her child. Once paternity has been established the father can petition for joint custody or visitation rights. A child support order will also be issued at that time. See the link provided below for a sample booklet on never married parents questions and rights in Massachusetts and a link for child custody laws in the US.
mother has sole custody, father has child support obligation. see link