Updated: Oct 20
Before we learn about Distant Kindred
It would be best you refer to "7 FUNDAMENTALS OF ISLAMIC INHERITANCE LAW" for dynamic and simultaneous application for calculating Islamic inheritance shares.
Distant kindred shares
Distant Kindred or Uterine relations or Uterine heirs are called Zav-il-Arham or Dhu al-Arham in Arabic. Distant Kindred can not be eligible when any Fixed sharer or Residuary is alive. The majority of Madhab agrees to give residue to Distant Kindred except for the traditional Maliki fiqh (Muwatta by Imam Malik, Book 27, Number 27.11.9 b). Those Madhabs who agree on qualifying Distant Kindred have the basis on the Holy Quran verse 4.33; "And We have appointed heirs to what has been left by parents and next of kin. As for those you have pledged to, give them their share. Surely Allah is a Witness over all things." Also, another verse of Holy Quran 33.6 states, "...Blood relatives are more entitled to inheritance than other believers and immigrants unless you want to show kindness to your close associates through a bequest. This is decreed in the Record."
The distant kindred determining eligibility rules are very complicated and differ among all four classes concerning every Madhab. Hanafi, Shafii, and Hanbali fiqh rely on Abu Yusuf and Abu Muhammed (may Allah show mercy on them both) for some portion of the distant kindred inheritance. They were Imam Abu Hanifa's lawyers and companions (may Allah shower mercy on him). However, the most common rules to gain an overall understanding are below.
Nearer in the degree to the deceased gets priority over the far in degree.
If they are equal in degree, the one claiming through sharer or residuary gets priority.
If there are males and females, then each male gets double the share of females. However, in some cases, both males and females are treated equally based on different degrees, genders, blood relations, and/or paternal and maternal sides.
In regards to different classes, the Shafii school differs from the Hanafis in the order between Ascendants and Descendants of the deceased (Refer to The Mahomedan Law of Inheritance according to the School of Shafii, Ch.V, The Uterine relations or Distant Kindred, Page-23 to 28 by C.H.Withers Payne).
Shafii and Hanbali use a representation system (i.e., Tanzil), whereas Hanafi Fiqh uses a blood relationship system (i.e., Qarabah). Distant Kindred do not inherit as per Maliki fiqh.
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...