If I do not have surviving Islamic heirs from my paternal side, who will receive my estate?

Let me provide some background.

Sharī‘a divides the Islamic heirs or Islamic beneficiaries of your estate into three categories:

1. Qur’anic heirs (ahl al-fara’id). Qur’anic heirs take a predetermined share—either one-half, one-quarter, one-eighth, two-thirds, one-third, or one-sixth. They are: Four males: Husband, maternal brother, father, and paternal grandfather Nine females: Wife, daughter, son’s daughter, mother, paternal grandmother, maternal grandmother, full sister, maternal sister, and paternal sister.
2. Residuary heirs (taking by taʿsīb). If there is anything left in the estate after the Islamic heirs take their prescribed shares, the residuary heirs inherit the balance. They do not have a fixed share. The residuary heirs are ranked in order of priority. For example, a son and daughter take any balance remaining after the prescribed shares. If there are no children, then the siblings take the balance remaining, if there are no siblings, then the nephews take the balance remaining and so forth.
3. Dhawūʾl l-arḥām.If no Qur’anic or taʿsīb heirs survive (a rare occurrence), then the estate goes to dhawūʾl l-arḥām. The most common translations are “distant kindred,” “uterine heirs,” or “outer family.” While spouses are Qur’anic heirs, they are not eligible to receive any balance or residue left if the estate is not exhausted, so the remainder of the estate will pass to distant kindred if there are no other Qur’anic heirs or residuary heirs.

If there are no surviving Qur’anic heirs or taʿsīb heirs (residuary heirs), the Ḥanbalī, Ḥanafī, and Shāfi’ī schools will distribute the estate to dhawūʾl l-arḥām. The Mālikī school, on the other hand, will distribute the estate to the public treasury. Modern Mālikī scholars, however, have concluded that in the absence of a true Islamic government, such as in the United States, the estate will be distributed to dhawūʾl l-arḥām.

There is no exact English translation for dhawūʾl l-arḥām. The most common translations are “distant kindred,” “uterine heirs” or “outer family.” Al-rḥām (plural: Al-ʾarḥām) means “to have mercy, compassion or sympathy.” In the Qur’an, it means “a familial relationship.” (Qur’an 4:1. Fear God in Whose name you make requests one of another, and sever not the ties of kinship [Al-ʾarḥām]. God watches well over you.). Juristically, dhawūʾl l-arḥām refers to relatives that are not Qur’anic heirs or taʿsīb heirs (residuary heirs). While spouses are Qur’anic heirs, they are not eligible to receive radd if there are other surviving Islamic heirs.

Muslim scholars divided a dhawūʾl l-arḥām–specific relative into one of three categories:

1. Descendants of daughters:

Children of your daughters and their children;

Children of your son’s daughters and their children;

2. Descendants of your father

Children of sister (both full or paternal) and their children

Daughters of brothers (both full or paternal) and their children

Children of maternal brother and their children

Daughters of male nephews (full and paternal) and their children

Maternal uncle – the decedent’s father’s brother from his mother, decedent father’s uncle, decedent’s grandfather’s uncle from his mother; and their children

Aunt (full, paternal or maternal), including decedent’s father’s aunts or grandfather’s aunts and their children

Daughters of uncles (full, paternal or maternal) and their children

Daughters of the son’s of uncles (full, paternal or maternal) and their children

Father’s mother’s father

Mother’s father’s father’s father

Father’s mother’s mother’s father’s father

Farther’s mother’s father’s father’s father

Father’s mother’s mother’s father

Father’s mother’s father’s father’s mopther’s father

Farther’s mother’s father’s father

Mother’s mother’s father’s father’s father

Mother father’s father’s father’s father

Aunt’s aunt (sharing father or sharing mother)

Father’s uncle (sharing mother)

Grandfather’s uncle (sharing mother)

3. Decedent’s of your Mother

Mother’s siblings and their children (full, paternal or maternal)

Mother’s mother’s siblings and their children (full, paternal or maternal)

Father’s mother’s siblings and their children

Mother’s aunts and uncle and their children

Father’s aunts and uncles and their children

Mother’s aunts and uncles and their children

Mother’s father’s father’s father

Mother’s father’s fathers’ mother

Father father’s mother’s mother

Father’s father’s mother’s mother’s mother

Mother’s Father’s mother

Mother’s father’s mother’s mother

Mother’s father’s father’s mother

There are three scholarly opinions on how to divide the estate to dhawūʾl l-arḥām beneficiaries.  The ʾahl al-rḥām method divides the estate equally between all of the dhawūʾl l-arḥām, irrespective of gender or generational class. The majority of scholars, however, have since rejected this opinion, despite its simplicity.  The ʾahlʾl-tanzil method divides the estate using distribution by representation. This means that a relative in the dhawūʾl l-arḥām group steps into the shoes of the Qur’anic heir or residuary heir relative and inherits what that relative would have inherited had he or she survived the decedent. The standard inheritance rules of prescribed shares, residue, and blocking apply. The Ḥanbalī, Mālikī, and Shāfi’ī schools adopted this opinion.  The ʾahl qaraba method divides the estate using distribution per capita. With distribution per capita, heirs of the same generation will each receive the same amount. The estate is divided into equal shares among the surviving heirs of the generation closest to the deceased.