Historically, there was a distinction between the Tayyibi and the Hafizi Musta'lis, the former recognizing at-Tayyib Abu'l-Qasim as the legitimate heir of the Imamate after al-Amir bi-Ahkam Allah and the latter following al-Hafiz, who was enthroned as caliph. The Hafizi view lost all support following the downfall of the Fatimid Caliphate: current-day Musta'lis are all Tayyibi.
