A more thorough explanation:

Equitable adoption is a legal concept that refers to the creation of a parent-child relationship between two parties who are not related by blood or adoption. This relationship is established by a court order and gives the adoptive parents all the rights and responsibilities of a biological parent.

Equitable adoption can occur in two ways:

1. When someone promises or acts in a way that precludes them and their estate from denying adopted status to a child. This is known as adoption by estoppel.
2. When a court issues an equitable decree of adoption treating as done that which ought to have been done.

For example, if a couple takes in a child and raises them as their own, but never goes through the formal adoption process, the child may still be considered equitably adopted if the couple promised or acted in a way that led the child to believe they were adopted. In this case, the child would have the same legal rights and responsibilities as a biological or formally adopted child.