What is "ilḥāq" (affiliation/annexation) and what are its conditions? What is the ruling on a son whose father acknowledged him, born to a woman with whom he lived as spouses without a formal marriage contract, knowing that she is seemingly unattached and they are considered spouses in the eyes of people?

Istilhāq is the claim of paternity for someone else. Its conditions are that the person for whom paternity is claimed (al-mustalḥaq) must not have a known lineage, and must not be a proven child of zinā (fornication/adultery). The proven child of zinā cannot have istilhāq applied to him, according to the majority of scholars, because Islamic law severs his lineage from zinā. Some scholars permit istilhāq for him if the woman was not married to anyone. A lawful marriage is one that fulfills its conditions of validity, and registration of the contract in official departments is not a requirement.