I found following regarding Emir Abu Taglib Fad'lallah of Mosul maybe someone having more information to add.
"The Hamdanids of Northern Iraq Hamdanid family tree in the Encyclopedia of Islam: Adi b. Usama ... b. Taghlib . . . Hamdun b. al-Harith | Hamdan b. Hamdun b. al-Harith | Abu l-Haydja (ruled 905-929)died 929 | Nasir al-Dawla (ruled 929-967) died 969 | Abu Taghlib (ruled 967-978)died 979 | bint ("daughter of") Abu Taghlib married Romanus Skleros
I was researching the story of the Hamdanid Emirs and came across a very in depth article about them in volume III of the Encyclopedia of Islam pages 126-131 which lists the father, grandfather, and great grandfather of the last Hamdanid ruler in Northern Iraq, Abu Taghlib. The article names his full name as "Fadl Allah Abu Taghlib al-Ghandanfar".Abu Taghlib deposed his father in 967 and ruled until 978 when Mosul was captured by the Buwayhid forces.He was executed in the year 979 after being taken prisoner by Mufarridj, the master of Ramla, Palestine. His father was "Al-Hasan b. Abd Allah b. Hamdan" who was also known as "Nasir al-Dawla."He had a very volatile reign from 929 until he was deposed by his son Abu Taghlib in 967.For about a year (942-943), Nasir al-Dawla made himself "amir al-umara" and controlled what was left of the Abbasid Empire until he was kicked out of office by a revolt led by one of his officers and returned to Mosul.After being deposed by his son in 967, Nasir al-Dawla was exiled to Ardumusht, where he died in 969. Nasir al-Dawla's father was "Abd Allah b. Hamdan" who was known as "Abu l-Haydja".Abu l-Haydja was governor of Mosul off and on from 905 until 929, when he became involved in a plot to make Muhammad al-Kahir Caliph of the Abbasid Empire.The plot backfired and Abu l-Haydja died "heroically" defending Al-Kahir. Abu l-Haydja's father was "Hamdan b. Hamdun b. al-Harith" who is first mentioned in the historical record as taking part in an army fighting against the Kharidjis of Djazira (northern Iraq). The article also states that "the Hamdanids are descended from Adi b. Usama ... b. Taghlib, which is why they are called Taghlibis and Adawis(see their genealogical tree in Wüstenfeld, Tabellen, C, 32 and in M. Canard, Histoire de la dynastie des Hamdanides de Jazira et de Syrie, i, Algers 1951, 287-8; cf. the appendix to the edition of the Diwan of Abu Firas by S. Dahan, Beirut 1944)," and further states that the family originated in Barkaid in the eastern part of the Djazira. The abbreviation "b." stands for the word "bin" which means "son of". It is a variation of the Arabic word "ibn" which also means "son." I hope this information will be helpful to any researchers of the Hamdanid family.
The article on Nasir al-Dawla on pages 994 and 995 names Nasir al-Dawla's Kurdish wife "Fatima bint Ahmad" as the mother of Abu Taghlib".