non-married custody situation

[tigger]

He doesn't indicate which state he's in but in NC:

"   Under state law, when a child is born to a married mother and father, that child is presumed to be a child of that marriage (North Carolina General Statute § 49‑12.1). This means that the father is automatically, in the eyes of the law, the legitimate father, and no further action is needed to establish paternity of the child.
     In contrast, when a child is born to an unmarried couple, a father's rights regarding that child are not immediately established. This is true even if the father is listed on the child's birth certificate. Paternity must first be established before a father can have any rights and obligations regarding visitation or support of his child.
     North Carolina statutes allow a child to be legitimized in one of two ways: through the subsequent marriage of the child's mother and father (North Carolina General Statute § 49‑12), or through the declaration made by the child's father to the court (North Carolina General Statute NCGS § 49‑10).
     Once paternity is established, an unmarried father has the same rights as a married father. This means a father has the right to visitation or custody of the child, as deemed appropriate by the court, and that the father has to fulfill support obligations owed to the child. If you are an unmarried father needing to establish your rights, contact your attorney for assistance through these court proceedings. "


Mother has immediate, continued and sole custody of the child. He has to establish paternity even if he's listed on the birth certificate and even then, he's not immediately granted the SAME rights as the married father, only that he's entitled as the court sees fit.

[OneMan]

He doesn't indicate which state he's in but in NC:

"   Under state law, when a child is born to a married mother and father, that child is presumed to be a child of that marriage (North Carolina General Statute § 49‑12.1). This means that the father is automatically, in the eyes of the law, the legitimate father, and no further action is needed to establish paternity of the child.
     In contrast, when a child is born to an unmarried couple, a father's rights regarding that child are not immediately established. This is true even if the father is listed on the child's birth certificate. Paternity must first be established before a father can have any rights and obligations regarding visitation or support of his child.
     North Carolina statutes allow a child to be legitimized in one of two ways: through the subsequent marriage of the child's mother and father (North Carolina General Statute § 49‑12), or through the declaration made by the child's father to the court (North Carolina General Statute NCGS § 49‑10).
     Once paternity is established, an unmarried father has the same rights as a married father. This means a father has the right to visitation or custody of the child, as deemed appropriate by the court, and that the father has to fulfill support obligations owed to the child. If you are an unmarried father needing to establish your rights, contact your attorney for assistance through these court proceedings. "


Mother has immediate, continued and sole custody of the child. He has to establish paternity even if he's listed on the birth certificate and even then, he's not immediately granted the SAME rights as the married father, only that he's entitled as the court sees fit.

Again, check your laws. State laws vary. Many (most) states, for example, no longer call unmarried children "illegitimate," so no legitimizing as in the quote about NC above.

Also, many states do give father SAME rights as married father. For example, if a father has acknowledged that he is the father on the birth certificate, then his rights are automatically established. This is different from a mother writing some man's name on the certificate herself.

How can a mother have "immediate, continued and sole custody of the child" even in NC once the father's paternity is established there? If a legal judgment is made giving the father sole custody or half custody, then sole custody would not continue for the mother.

GA is the same as NC. According to one GA law blog:  If custody is to be an issue, father must still file legitimation first, and get the Order of Legitimation signed. Once child has been legitimated by the Court Order then father may file another action for custody. The exception to this rule is if the mother is deceased, there is no other legal parent or guardian, or the mother consents to custody. If father is already listed on the child's birth certificate as the father, but father and the child's mother were not married to one another, father must still file a petition with the court to legitimate his child.

[ocean]

Same in NY:
If father was never married to mother, he must prove paternity either by test through the courts or signing the paternity form in the hospital. After that, father has to file custody and visitation papers. Father will get joint legal custody here BUT will not get joint physical custody ordered unless the parents worked that out. It is very rare here for fathers to get more than the standard visitation. Sad but still true with the family court system.

[OneMan]

Same in NY:
If father was never married to mother, he must prove paternity either by test through the courts or signing the paternity form in the hospital. After that, father has to file custody and visitation papers. Father will get joint legal custody here BUT will not get joint physical custody ordered unless the parents worked that out. It is very rare here for fathers to get more than the standard visitation. Sad but still true with the family court system.

Yes, NY state is well-known for remaining in the dark ages when it come to fathers, married or unmarried.

When it comes to unmarried parents, the law has the unintended consequence of promoting a situation where a child is cut off from his or her father because the mother refused to marry the father after he got her pregnant. If she doesn't want the father in the child's life, the court will probably side with her, even though the father had asked her to marry him once she became pregnant or after the child was born.

Not a child-friendly law, to be sure.

In any case, these laws vary by state. According to one website:

"In states like Michigan (http://singleparents.about.com/od/childcustodylaws/a/michigan_child_custody_laws.htm), it is presumed that an unwed mother only has initial custody — as opposed to sole custody — even when the father is not on the birth certificate and has never signed a formal acknowledgment of parentage. 
"You should be aware, as well, that many states either make no presumption of custody based on whether the father is on the birth certificate, or presume joint custody even in cases where the parents were never married."