This is a legal process involving a court hearing during which a judge issues a decree that permanently ends all legal parental rights of a birth parent to a child. This must occur before a child is considered to be legally free for adoption. Termination of parental rights can be voluntary or involuntary, that is, with or without the birthparents' agreement. In some states, there is a period during which the birthparent may appeal, if rights have been terminated without his or her consent. The length of that period varies from state to state.
When my wife and I adopted our son, we were told that we needed to hire multiple attorneys. One to represent the birth mother. One to represent the child. One to represent the birth father. And one to represent us. When we adopted our daughter we needed even more. One for the child. One for the birth mother. One for us. And one for each of the three possible birth fathers! We were outnumbered! Since no agency was involved, the attorney fees, the home study and the court costs were our only expenses. And when it came time to file our income taxes we claimed the adoption tax credit and were reimbursed the entire amount. Both times. We were fortunate. Adoptions can be, and in most cases are much more expensive.