The Girays of the Crimean Khanate are regarded by some as the second family of the Ottoman Empire after the House of Osman it's self. Sebag Montfiore's book of Potemkin, an important advisor to Catherine II of Russia asserts: "If Rome and Byzantium represented two of the three international traditions of imperial legitimacy, the blood of Genghis Khan was the third... If ever the Ottomans became extinct, it was understood that the Genghisid Girays would succeed them."
The Ottoman line it's self never seemed very close to going extinct, but still -- was this true? If the Ottoman line had went extinct, would the Girays succeed them? I'm talking more in the early modern period, when the Girays still ruled over the Crimean Khanate, possibly in the 17th century. Was it an unspoken agreement? If the Ottoman line went extinct, would the House of Giray be welcomed into Instanbul, no questions asked?
I know this has been discussed before, but I haven't been able to find any of the topics on it. If the Ottoman line went extinct sometime in the 17th century, what would be the ramifications, especially regarding the Girays. Is their gaining the throne plausible? If not, what would be a likely consequence? If they do gain the Ottoman Throne, might effects might this have on the empire politically, socially, and culturally?