Acknowledgment of paternity

What does Acknowledgment of paternity mean in American Law?

The definition of Acknowledgment of paternity in the law of the United States, as defined by the lexicographer Arthur Leff in his legal dictionary is:

An acknowledgment, but one carrying less [of] an implication of any need for a formal, intentional, deliberate act. A child may be acknowledged as one’s own with all the formality of a sworn affidavit or an admission in open court, but more casual verbal statements, or even conduct toward and treatment of the putative descendant, will sometimes work an acknowledgment of paternity. The establishment of the relationship is important, of course, in divers legal contexts, e.g., claims for rights to intestate succession, support, etc.