perhaps the Ismailis on the board would like to elaborate/correct/chastise...
Sorry that took me so long.
The splits in the Shia branch mostly arose because of disputes over who would be the next Imam, or spiritual leader of the entire faith.
You forgot the Zaydis, but then one could say that they're not a major Shia division. In 732 CE, the third Shia Imam Zainul Abideen had two sons. Those who followed the younger -- Zaid -- are called the Zaydis. They are found mostly in Yemen.
Then there are some divisions of the Ismailis that are no more, or else they are very small. The "Druze" (Northern Lebanon), the Mustaalis, the Momin Shahis (around 4000 in Syria)... thus, taking all of these splits into account, today's Ismailis are "Shia Imami Nizari Ismaili Muslims," but since we're the only Ismailis around, that's what we're called.
As to whether the Ithna'asharis of the Ismailis form the majority, current numbers show the Ithna'ashari are around a 60-80% majority, IIRC, but there are known to be a significant number of Ismailis in the Northwest of China. Some people say that Chinese Ismailis could actually form the majority of Ismailis world-wide, but I'm not as optimistic about that.
More to come later. I'm tired....