To take as one own.
To put forward as if it were your own, and be responsible or liable for something issue of another person.
One municipal or local government may adopt a by-law being proposed, thereby making it their own; "adopt connotes ... approval or acceptance".1
Used mostly in family law to refer to the legal and formal acceptance of another's natural or biological child as if that child were your own, with the same rights and responsibilities attached thereto as if the child were your naural child, both in terms of child support and standing in intestates.
A creature of statute2 and a fairly novel concept to English law, adoption is usually governed by local law such as state (USA) or provincial (Canada).
"In English law, the making of an adoption order effects the transfer of a child into a different family group and by that order extinguishes the parental responsibility prviously held by the child's former parent or parents who are not members of the child's new family group."2
Ontario's Child and Family Services Act contains an entire Part 7 dedicated to the process of adoption.
In the USA, by way of further example, Alabama has several Chapters (10, 10A, 10B and 10C) of it's state code on topic, dealing with adoption, subsidizatiion of adoption, and interstate adoption processes.
References:
► Child and Family Services Act of Ontario at canlii.com/on/laws/sta/c-11/index.html
► Code of Alabama, at legislature.state.al.us/CodeofAlabama/1975/coatoc.htm
1. Thomas v BC 1996 139 DLR 4th 685 (BCPC).
2 . Halsbury's Laws of England, 4th Ed., Volume 5(3), p. 241.