Map of the approximate borders of the Empire of Trebizond shortly after the establishment of the Latin Empire, with the short-lived possessions in western Anatolia conquered by David Komnenos – map by Samhann for Wikipedia “Empire of Trebizond” licensed under https://creativecommons.org/licenses/by-sa/4.0/
(9) EMPIRE OF TREBIZOND & PRINCIPALITY OF THEODORO
(1204-1461 / 1475 AD)
One of the three major residual successor states to the eastern Roman Empire after the fall of Constantinople to the Fourth Crusade in 1204 – and the one with coolest alternative name, the Trapezuntine Empire.
(Which always prompts to my mind images of the Trapezoid Empire, itself prompted by that pyramid scheme in The Simpsons protesting that their model was more of a trapezoid).
Like the other two vestigial states, it claimed to be the legitimate successor of the eastern Roman Empire – but pushed that claim the least of the three of them, preferring to do its own thing on the Black Sea coast and peacefully abandoning its claim in 1281 or so by treaty with the Nicene imperial state that did succeed in claiming back the empire.
Interestingly, the Trapezuntine Empire was formed before the fall of Constantinople, essentially as a descendant of the last truly great imperial dynasty took the opportunity presented by the encampment of Crusaders outside Constantinople for a military adventure to found his own empire, in alliance with the kingdom of Georgia.
Before that, Trebizond had a long history of doing its own thing even when part of the Roman empire and the Trapezuntine Empire just carried on that history, only more so through the wealth of its trade and pimping out its princesses famed for their beauty.
And there must be something to that foreign policy of bling and booty as Trebizond survived longest among the eastern Roman successor states (setting aside the residual Serbian or Italian dependency that was in Epirus), outlasting the fall of Constantinople until it too was besieged and conquered by the Ottomans in 1261.
Even then, its bizarro Byzantine offshoot in a sliver of Crimea, the Principality of Theodoro, lasted another 14 years until it too fell to the Ottomans in 1475.