Abbasid Caliphate
During the period of the Abassid dynasty, Abassid claims to the caliphate did not go unchallenged. The  Ubayd Allah al-Mahdi Billah of the Fatimid dynasty, which claimed descendency of Muhammad through his daughter, claimed the title of Caliph in 909 and created a separate line of caliphs in North Africa. Initially it covered only Morocco, Algeria, Tunisia and Libya, but then the Fatimid caliphs extended their rule for the next 150 years, taking Egypt and Palestine and even ancient Pakistan, before the Abbassid dynasty was able to turn the tide, limiting Fatimid rule to Egypt. The Fatimid dynasty finally ended in 1171. The Umayyad dynasty, which had survived and come to rule over the Muslim provinces of Spain, reclaimed the title of Caliph in 929, lasting until it was overthrown in 1031.