Let me elaborate; what I'm specificly looking for is a caliphate after the collapse of the Abbasids. For the purposes of this thread, I'll outline my requisites for a nation to be a "Caliphate".
1). The nation contains a majority of the Muslim world during it's existance
2). The Caliphate holds the holy cities of Medina and Mecca.
3). It recongnizes itself as a Caliphate; and the state religion ofcourse must be Islam.
For the sake of the topic, you can ignore West Africa and Indonesia as parts of the "Muslim World".
So with that aside, did any nation come close to becoming a true Caliphate? Should the Ottomans be considered a Caliphate? What nation or people could have established itself as a caliphate?
While I ask for something post-Abbasid Caliphate, ones before them will also be appreciated.