Ever wonder why Isma'ilis are referred to as "Seveners", even though they have many more imams that they believe in? That's because the pre-Fatimid Isma'ili da'wat taught that there were only seven Imams, the seventh being Muhammad b. Isma'il b. Ja'far whom they claimed was the Qaim, was in ghayba, and who would re-appear immanently. This was propagated from some generations until one of their da'is, Sa'id b. al-Husayn, claimed that in fact he was the Imam himself claiming descent from Muhammad b. Isma'il. This split the da`wat into those who thought this was nonsense, and held on to the seven-imam theory (the Qaramita), and those who followed Sa'id. To explain the discrepancy, the da`wat then explained that the whole thing about Muhammad b. Isma'il had really just been a ruse to throw off their enemies, and that he was more a symbol of the general rising of the imams (i.e. Sa'id b. al-Husayn and so on.).
Sa'id, aka 'Ubaydullah al-Mahdi, through the missionary work of Abu 'Abdullah ash-Shi'i established himself in North Africa (leading to the establishment of the Fatimid dynasty. Abu 'Abdillah however after his work for him, was disappointed with his erstwhile master and fell out from him, and was put to death.) The Fatimid ruled their dynasty (with its ups and downs, including the very erratic sixth Fatimid Caliph, al-Hakim) until the death of al-Mustansir. Now, this latter had apparently designated his eldest son (by this time an adult) an-Nizar to succeed him to the throne. The vizier, al-Afdal, however had different plans, and placed al-Mustansir much younger son who was then a child, Ahmad (aka al-Musta'ili), on the throne with him ruling behind the scenes. Nizar was thus deposed, and eventually apparently died in prison. al-Musta'li was eventually succeeded by his son, al-Amir (then five years old), with al-Afdal continuing his role of power. Eventually, al-Amir grew tired of this, and had al-Afdal (the one who placed his father on the throne) killed. al-Amir himself eventually got assassinated (notice there was quite a lot of that amongst the Fatimids?), and did not have an apparent successor. His cousin al-Hafiz then eventually rose to the throne, and it's at this point that the da`wat in Yemen decided to break off from the Fatimids, claiming instead that al-Amir had a son named Tayyib who had gone into ghayba, and that now power had been transferred to the da`i al-mutlaq (absolute da'i). From that time the Musta'li lines continue to this day.
However, in this period now of successive da'is you get eventual splinters amongst them, with rival claimants to the position of da'i al-mutlaq. The OP belongs to the Dawoodi branch which is based in India, while the Sulaymani branch is based in Yemen. The Dawoodis themselves split a number of times, with one of their worst crises being after the sudden death of their 46th da'i, Muhammad Badr ad-Din, without having pronounced a successor. So what did they do? Well a group of their 'ulama appointed Abd al-Qadir Najm ad-Din to act in a caretaker role to the da'wat. What did he eventually do? Pronounce himself to be the da'i al-mutlaq... Nowadays the Dawoodis are run by their da'i (who apparently claims to be infallible now), from whom they have to obtain permission for much of the affairs of their life, only being allowed to study the deeper religious material with his approval (which is hard to obtain). The Dawoodi da'wat is largely a family affair now, with relatives of the da'i holding many of the positions of power over their community.
