What is the process to have a mother’s parental rights terminated?

In order to terminate a parent's rights as to a child completely there has to be a formal adoption of the minor child where one parent voluntarily gives up his or her parental rights via a signed adoption agreement subject to court approval.

Such an adoption agreement is usually prepared by a family law attorney.

The state of Pennsylvania only allows the termination of parental rights  - voluntary or involuntary - to be done by court order. For having them involuntarily terminated, Pennsylvania requires that a petition be filed.   Then the court must be satisfied by clear and convincing evidence one or more of the following: (1) the parent has demonstrated a purposeful abandonment of the child for at least six months; (2) the parent is shown to have continued incapacity or has abused, neglected or refused to provide the child with essential care, control or subsistence necessary for the child's physical or mental well-being and those conditions are not likely to be remedied by the parent; (3) the parent is the presumptive but not the natural father of the child (4) the child is in the custody of an agency, and the parent's identity or whereabouts are unknown and cannot be determined within three months after the child is found; (5) the child has been removed from the care of the parent and placed with an agency for at least six months, the conditions which led to the removal continue and are not likely to be remedied; (6) the parent of a newborn has reason to know of the child's birth, does not reside with the child, and for four months preceding the filing of the petition has failed to make reasonable efforts to make contact with the child or provide substantial financial support for the child; or (7) the parent is the father of a child conceived as a result of a rape or incest.  Seek help.