[continuing from OED]
" After 13th cent. many of the popular words were refashioned with -at,
as sené, senat, avoué, avocat; and all new words have been thus formed,
e.g. assassinat, attentat, épiscopat, palatinat, professorat, syndicat.
In English these were originally adopted in their French form, estat,
prelat, etc.; after 1400, -e was added to mark the long vowel, estate,
prelate, etc., and all later words from French took -ate at once. After
these, English words are formed directly on Latin, as curātus ‘curate,’
or on Latin analogies, as alderman-ate, cf. triumvir-ate. In meaning,
words in -ate are chiefly:
a. Substantives denoting office or function, or the persons performing
it, as marquisate, professorate, episcopate, syndicate, aldermanate."
...so with other exotic rulers: sultanate, emirate, probably others...