Do most Muslims want a caliphate?

Yes, most Muslims do want a Caliphate - through most of their history, their lands had the caliphate, which lasted until 1924 when the Ottoman caliphate was destroyed. Maryland University's 2007 and 2011 surveys found similar opinion ratings. In Egypt, Morocco, Indonesia and Pakistan, majorities said they agreed to the establishment of a new Caliphate and the strict application of Shari'a law. Pew Research Centre, whose surveys Esposito and Mogahed had reviewed, had posed that very question.  It was found that overwhelming percentages of Muslims in many countries had stated they wanted Islamic law (Shari'a) as the official law of the land. Support was highest in South Asia (median of 84%). Majorities of Muslims in sub-Saharan Africa (64%), the Middle East-North Africa region (74%) and Southeast Asia (77%) also favoured Shari'a as official law. Across the countries surveyed Pew Research Centre found many Muslims who said their laws did not follow Shari'a believed this to be a bad thing. Muslims in South Asia were especially likely to express this sentiment with Pakistan (91%), Afghanistan (84%) and Bangladesh (83%). Pew also found many Muslims want religion to play a prominent role in politics. Majorities in Southeast Asia (79%), South Asia (69%) and the Middle East and North Africa (65%) say religious leaders should have at least some influence over political matters.