Madhab refers to Sunni Islamic schools of jurisprudence. There are four Sunni Madhab; Hanafi, Shafii, Maliki, and Hanbali. All Madhab (Sunni Islamic Jurisprudence) have domination and influence worldwide where Sunni Muslims dwell. One Imam does not claim their opinion to be superior compared to the other Imam’s opinion; instead emphasizes going back to the Holy Quran and Sunnah. All Madhab agree on the law of inheritance in Quranic shares, rules, and conditions. The minor opinion differences are derived through Ijma (i.e., Consensus of leading companions of beloved Prophet Muhammed Sallallahu Alayhi Wasallam) and Qiyas (i.e., Analogical deductions). There is no difference of opinion on marriage or consanguinity but differs in the numbers of Asbhah al-furud (i.e., fixed or prescribed sharers) entitled to receive a share regarding al-Asbat (i.e., Residuary) and capacity to inherit under Dhul al-Arham (i.e., Distant kindred). However, some of the variations may impact shares and calculations you should know as below.
Paternal Grandmother (i.e., Mother of Father how high soever) does not receive a share if Father is alive as per Hanafi, Shafii, and Maliki but receives a share as per Hanbali.
Full and Paternal Siblings do not receive a share if the Paternal grandfather (i.e., Father of Father how high soever) is alive as per Hanafi law of inheritance but receive a share as per Shafii, Maliki, and Hanbali.
Radd is allowed according to Hanafi and Hanbali, but it is not permitted under Shafii and Maliki. Radd has to go to Bayt-Ul-Mal (i.e., Islamic Treasury or Charity) as per Shafii and Maliki. Maliki allows Radd if Byat-Ul-Mal (i.e., Islamic Treasury or Charity) is not functioning properly. Radd is one of the scenarios when the Total succession share is less than ONE, i.e., less than 100%. All shares except spouse shares are increased proportionally to make the Total share 1 or 100%.
Paternal Grandfather (Father of Father) surviving with Full or Paternal siblings and their descendants share calculation differs among different Madhab including Shafii, Maliki, and Hanbali on some special situations; Al-Himariyyah, Al-Akdariya case or Paternal Grandfather surviving only with Paternal Sisters, etc.
Traditionally, Hanafi, Shafii, and Hanbali allow the Dhul al-Arham (i.e., Distant kindred) shares, but Maliki does not allow them. This statement is correct regarding the Maliki opinion about Dhul al-Arham, but some believe that this ruling applies when the ruler is just and fair. If the ruler is not just and fair and misappropriates the treasury, then the wealth will be given to Dhul al-Arham.(Hashia Dusooqi al alsharhelkabeer, Vo:4, page: 468,). Also, The Shafii opinion does not favor giving a share to Dhu al-Arham. There are two opinions in Shafi fiqh; according to one opinion, Dhu al-Raham will not get any share, while according to the other opinion, Dhu al-Arham will receive the succession only in the absence of Bait al-Mal. If the Bait al-Mal is present, Dhu al-Arham will not get any share (Al Muhazzab: V:2,page:419) (Rauzatuttalebeen: V,5 page:8).
Hanafi has different schemes for calculating the shares for distant kindred based on Imam Muhammad's and Imam Yusuf's opinions (Allah may be pleased with them both). On the other hand, Shafii and Hanbali use the method of "Representation" called (i.e., Tanzil). All of these schemes will give different outcomes.
Regarding the "Zakat" or "Zakah," Muslim jurists have different opinions regarding paying the Zakat from the deceased person's property. According to the majority of fuqaha, it is obligatory to pay Zakat first, and then the residue will be distributed among the heirs. In comparison, the Hanafi school believes that it is not obligatory. Hanafi school opines that the Zakah will not be deducted because the deceased person is no more aptitude to execute any contract or fulfill a religious duty. Durr Al-Mukhtar and Hashiyat Ibn Abidin (Redd Al-Mukhtar) (6/760): “(Then) he gives precedence (his debts that have demands on the part of the servants), and he gives precedence to the debt of health over the debt of illness if the cause of it is not known; otherwise it will be forgotten as the master explained it. (His saying: As for the religion of God Almighty, etc.) Beware of his saying: On the part of the servants, such as Zakat, penances, and the like. Al-Zayla’i said: They fall by death, so the heirs are not obliged to pay it unless he recommends it; or donated by themselves; Because the pillar in the acts of worship is the intention and action of the obligated one, and he has passed away with his death, so he cannot be imagined.
Madhab's opinions differ on many special situations, such as newborns, stillborns, missing persons, drowned persons, burned persons, hermaphrodites, Simultaneous deaths, unintentional killing, Gestation period limits, etc.
Allah, the Most Glorified and the Most High, knows the best. As a human, We are limited to everything and can not perceive it in totality...