Paternity means fatherhood and establishing paternity is the legal process of determining who's the father of a child.  If the parents are married, paternity is a given in most cases.  If they're not, the Paternity Opportunity Program (POP) provides a man the way to officially say, "Yes, this is my child," by signing a form called a POP Declaration, thereby establishing paternity.  There are lots of benefits to establishing paternity for parents and children - legal, financial, mental and emotional.  

Power of 2
The Hows and Whys of the Paternity Opportunity Program.

El Poder de 2
El proceso y los beneficios del Programa de Oportunidad de Paternidad.

The California Department of Child Support Services provides forms all the information you need to establish paternity.