To what extent (if any) does the Catholic Church recognize adoption?

Assuming the Church recognizes adoption, if a man or woman were to invite another to live together as a loving relationship as parent and child, but without any secular legal process, would the Church recognize the adoption? I ask this because some Catholics in history and today have lived/live in a land where there is no secular legal process to recognize an adoption. If the legal document is required, why does secular law have such an impact on Church teaching? (In some countries adoption is completely illegal.) By "recognize" I mean if it would be a mortal sin if at some point in time the 2 parties changed their minds on the nature of the relationship and decided to get married, or the parent giving up and cutting all ties with the child. So the adoption being just as permanent and having the same dignity as a biological parenthood.