OOC:The various rulers of that territory at least officially declared loyalty to Ogodei, Guyuk, and Mongke, and were relatively loyal to them. Even after Kublai lost all real loyalty, he and his son Temur had at least official leadership of those khanates.
OOC: I meant Mongke. I typed Hulagu, who died after Mongke did, by accident when I was looking up the Il Khanate, and the post has been edited accordingly, although you should probably have looked at the date (1259) and realized that I made a mistake. Kublai and his successor, Temur, might have had some influence over the others, but the fact that there was a succession dispute between Kublai and Ariq Boke from 1260-4 in the east, simultaneously along with a civil war between Berke and Hulagu during 1262 in the west, essentially demonstrated that the Mongols were no longer unified. In other words, although the Mongols might have remained generally united under a single ruler even after 1259, various military conflicts within the empire, beginning in 1260, suggests that political unity essentially ceased to exist.