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Paternity Suit from WikiPedia:

In law, paternity is the legal acknowledgment of the parental relationship between a man and a child usually based on several factors.

At common law, a child born to the wife during a marriage is the husband's child under the "presumption of lawful paternity", and the husband is assigned complete rights, duties and obligations as to the child. The presumption, however, can be rebutted by evidence to the contrary, at least prior to a formal court ruling involving the putative paternity (often this is a decree of divorce, annulment, or legal separation). Jurisdictions differ widely on when a judgment establishing paternity or a support obligation based on the presumption can be set aside on the grounds that the husband was not in fact the father.

In the case of an unwed mother, a man may come forward and accept the paternity of the child, the mother may petition the court for a determination, or paternity can be determined by estoppel over time.

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