Safe Haven Law
A Safe Haven Law is a law (either within a country or a sub-jurisdiction, such as a state) which allows the parent of a newborn (generally, the mother, and usually a young unmarried girl) to voluntarily "turn over" a newborn infant to the state (and thus irrevocably surrender parental rights to him/her) without fear of legal action (i.e. child abandonment charges), provided that (depending on the specific law) the newborn is turned over within a given period after birth and at a specified location (such as a hospital, fire station, or police station).
The law may also be titled a Baby Moses Law after the Old Testament story, or named for an abandoned infant in the state who's story led to the law's passage. The first such law was passed in Texas in 1999.
Another option which is becoming popular (due to the parent not wanting to be seen, often in a small town where people usually know everyone else) is a baby box, a specially-designed and built unit within a building (similar to a night drop off box at a bank, although considerably larger) where a mother can leave a newborn anonymously, placing the infant in the baby box triggers a silent alarm for a responder to retrieve the baby (from the interior of the building). The concept of baby boxes has been around for centuries in many countries, but in the United States gained renewal in Indiana due to the efforts of Monica Kelsey, who herself was abandoned at a hospital in 1973; Kelsey operates a non-profit organization (Safe Haven Baby Boxes) which seeks to install these units nationwide (Kelsey and her husband hold a patent for the box's design).
The laws are generally seen as positive, due to their intent to prevent the babies from being killed or abandoned, if or when the girls felt overwhelmed or without family support, as well as to reduce the pressure for late-term abortions. However, some people argue that the non-relinquishing parent does not get a say in the matter (and may not even know that a turn over has happened), and that the state can become a partner to dishonesty against the non-relinquishing parent, since the law makes termination of parental rights automatic upon the turn over, whereas in a traditional adoption both parents must voluntarily agree to terminate parental rights (though one or both parents can arrange for an open adoption and still maintain contact with the child).