Hajb — when does one heir shut another out?

Agreed. The core is agreed, and the agreement is recorded as such. Hajb is the exclusion of one heir by the presence of another. The jurists first separate it from a bar: a killer, or an heir of a different religion, is not ‘excluded’ but disqualified — the relationship is there and the entitlement is cancelled. True hajb has two grades. Hajb hirman drops the heir entirely: a grandson takes nothing while a son lives, an uncle nothing while a brother lives, the more remote grandmother nothing while the nearer survives. Hajb nuqsan only moves the heir down: a husband from a half to a quarter and a wife from a quarter to an eighth once there is a child; the mother from a third to a sixth once there is a child or two or more siblings; a son’s daughter from a half to a sixth beside a daughter; a consanguine sister from a half to a sixth beside a full sister. Six heirs are beyond total exclusion altogether, and the Mawsu’a states this twice with the word ijma‘an: the two parents, the two spouses, and the son and daughter — the test being that each of them reaches the deceased directly, with nobody standing in between who could block them. Ibn Qudama gives the same list in the Hanbali text, counting it as five because he takes son and daughter together, and gives the same reason. Two refinements complete the picture and are also reported as agreed. A person who is barred — the killer, the non-Muslim, the slave — blocks nobody at all, neither wholly nor partly, “because his existence is as his non-existence”; the Mawsu’a attributes that to the jurists at large “and among them the four imams” and works an example it resolves “by the agreement of the four imams”. But a person who is merely excluded can still cut somebody else down: brothers who take nothing because the father survives nevertheless reduce the mother from a third to a sixth. On the definition itself the Mawsu’a adds the sentence that makes this an agreement rather than a silence: after giving al-Sirajiyya’s Hanafi definition it says “the definitions in the other schools do not depart from this one”. We checked this point; the schools do not differ on it.

Shared evidence: al-Mawsu’a al-Fiqhiyya al-Kuwaytiyya, entry “Hajb” sec. 3 — “wa huwa la yadkhulu ‘ala sittatin mina al-warathati ijma‘an, wa humu: al-abawani wa’l-zawjani wa’l-ibnu wa’l-bint” — total exclusion never reaches six of the heirs, by consensus · al-Mawsu’a, entry “Irth” sec. 54 — the same six ijma‘an, and, on the definition of hajb, “wa la takhruju al-ta’rifatu fi’l-madhahibi al-ukhra ‘an hadha al-ta’rif” — the definitions in the other schools do not depart from this one; and that a barred heir excludes nobody “‘inda jumhuri al-fuqaha’i, wa minhumu al-a’immatu al-arba‘a” · al-Mawsu’a, “Irth” sec. 54 cont. — the worked case of a non-Muslim son, a wife and a full brother, resolved “bi’ttifaqi al-a’immati al-arba‘a”, and the counter-rule that one excluded by a nearer heir may still reduce another’s share · al-Mawsu’a, “Hajb” sec. 3 cont. — the three rules of hajb and their application; of the full brother’s exclusion by the father, the son and the son’s son on Q 4:176: “wa hadhihi al-mas’alatu mujma‘un ‘alayha bayna al-fuqaha’” · Ibn Qudama, al-Mughni — “wa man la yasqutu bi-halin khamsatun: al-zawjani, wa’l-abawani, wa waladu al-sulb; li-annahum yamuttuna bi-anfusihim min ghayri wasitatin baynahum wa bayna al-mayyiti yahjubuhum” — the same rule and the same reason, in the Hanbali text · Surah an-Nisa 4:11 (Khattab, The Clear Quran) — “if you are childless and your parents are the only heirs, then your mother will receive one-third. But if you leave siblings, then your mother will receive one-sixth” — the Qur’anic instance of hajb nuqsan · Surah an-Nisa 4:12 — the husband’s half falling to a quarter and the wife’s quarter to an eighth once there is a child.

Not covered by this finding: the one configuration where the schools genuinely divide over who excludes whom — a grandfather beside full or consanguine brothers and sisters, where Abu Hanifa excludes them and the other three schools do not. That is researched separately; this entry does not settle it. Nor does this entry cover the impediments themselves (killing, difference of religion), which bar an heir rather than exclude him, or the position of distant kin — not yet researched school by school. Treat that as open and ask a scholar of your school.