A woman who gives birth with the intention of raising  the child is conclusively the presumed mother even if she later abandons the child.  In re D.S. (2012) 207 Cal.App.4^th 1088.

However, where the natural mother is dead, a woman may achieve presumed mother status when she is able to demonstrate that she has held the child out as her own child and accepted the child into her home.  In re Salvador M. (2003) 111 Cal.App.4^th 1353.

A presumed father/parent is a person whom the law presumes to be the legal father/parent of the child with all of the attendant rights and responsibilities.  A presumed father/parent may or may not be the child’s biological father/parent.

Family Code Section 7611 defines presumed father:

1. The parents were married and cohabiting at the time of conception.
2. The parents signed a Voluntary Declaration of Parentage (see section above) or attempted to marry.
3. The presumed parent and the child’s natural mother are (or have been) married to each other and the child is born during the marriage, or within 300 days after the marriage is terminated by death, annulment, declaration of invalidity, or divorce, or after a judgment of separation is entered by the court.
4. The presumed parent and the child’s natural mother attempted to marry each other before the child’s birth by a marriage solemnized in apparent compliance with law, although the attempted marriage is or could be declared invalid, and any of the following is true:
   1. The child is born during the attempted marriage or within 300 days after its termination by death, annulment, declaration of invalidity, or divorce.
   2. The child is born within 300 days after the termination of cohabitation.
5. The parents married after the child’s birth and:
   1. The presumed parent is named as the child’s parent on the child’s birth certificate.
   2. The presumed parent is obligated to support the child under a written voluntary promise or by court order.
6. The presumed parent receives the child into his/her home and openly holds out the child as his/her natural child.

Presumed parents are entitled to reunification services if they request placement or custody of the child.
Welfare and Institutions Code Section 361.5(a)

A child may have more than one presumed parent.  In such cases the court is required to weigh the competing claims and determine which claimant should be recognized as the legal parent.
Family Code Section 7612(b)

In an appropriate action, a court may find that more than two persons with a claim to parentage are legal parents if the court finds that recognizing only two parents would be detrimental to the child.
Family Code Section 7612(c)

A “Kelsey S.” father was defined in a California Supreme Court case, Adoption of Kelsey S. (1992) 1 Cal. 4^th816.  A “Kelsey S.” father is a biological father who (1) is prevented by the other or a third party from establishing a parent-child relationship and (2) promptly acts to assert the parent/child relationship once the father knows or should have known of the existence of the child.  To be considered a “Kelsey S.” father, the parent must demonstrate a full commitment to his/her parental responsibilities, emotional, financial and otherwise after discovering the existence of the child.  Adoption of Kelsey S. (1992) 1 Cal. 4^th816; In re Hunter W. (2011) 200 Cal.App.4^th 1454.

A Kelsey S. father/parent is entitled to reunification services and has the same constitutional protections and due process rights in dependency proceedings as presumed parents.
Welfare and Institutions Code Section 361.5(a).

Even though a father may be biologically related to the child he does not have legal rights and responsibilities to that child in a juvenile dependency case.  A biological father is entitled to notice of dependency proceedings and the right to appear in court but is not automatically entitled to reunification services.  However, a biological father may be offered reunification services if the court finds that it would benefit the child to do so.
Welfare and Institutions Code Section 361.5(a)

A biological father is a father who is genetically related to the child but who has failed to take any steps to become a presumed father.  Michael U. v. Jamie B. (1985) 39 Cal.3d 787.

If a biological father appears promptly upon notice of the dependency case, he has the right to develop a relationship with the child.  In re Julia U.  (1998) 64 Cal.App.4th 532.

When a biological father wishes to assert his paternity post termination of reunification services, he must file a Welfare and Institutions Code Section 388 petition and must show the court that recognizing his paternity would be in the child’s best interest.  In re Vincent M. (2008) 161 Cal.App.4th 943.

An adjudicated parent is one who has an existing judicial determination that a parent/child relationship exists.  A paternity judgement does not establish presumed parent status but it may rebut a presumption of paternity in favor of another man.

An adjudicated father has established paternity so he is treated as a biological father. He may be granted reunification serviced but is not entitled to them if, and only if he can persuade the court that such reunification services will benefit the child.

An alleged father is a man who may be the father but whose biological paternity has not been determined and who has not been found to be presumed by the court.
Family Code Section 7630

Alleged fathers have the right to notice of dependency proceedings, the right to appear before the court, and the right to assert their interest in the child by filing a Statement Regarding Parentage form JV-505.  An alleged father is not a full party to the case and does not have a right to custody or reunification services unless and until his parentage is established.

An equitable parent is a non-biological parent who attempts to take full responsibility for the child but who is prevented from doing so by the mother or a third party.  In the Jerry P. case, the father supported the mother through her pregnancy and visited the baby every day while it was in the hospital.  The baby was abandoned by the mother.  CPS prohibited this father from bringing the baby home. He appeared at every hearing, sought presumed father status, completed parenting and CPR classes.  On appeal, he was determined by the reviewing court to have done all the things required for a biological father to be a father with Kelsey S. status. He had an existing familial relationship with the child; he demonstrated a loving, nurturing, parental relationship with the child; and he had been prevented from physically bringing the child into his home by a third party.  In re Jerry P.  (2002) 95 Cal. App. 4th 793.

A registered domestic partnership is a legally binding contract entered into by two people who want to formalize their relationship without going through a marriage ceremony.  Registered domestic partnership is available to all same sex couples and to a heterosexual couple if one partner is at least 62 years of age.  Partners may register by filing the Declaration of Domestic Partnership form NP/SF DP-1 and submitting it with the appropriate fee to the Secretary of State.

If parents are in a registered domestic partnership when a child is born, the law assumes the domestic partners are the legal parents of the child.

And, of course, a legal parentage is established by adoption.