The Roman empire being a long-lived empire and over a large area is likely to have had some dynasties/emperors that were not ethnically Latin/Italian, is that in fact the case? If so which dynasties/emperors?
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There is a fine list here: http://historum.com/ancient-history/19034-national-ethnic-origins-roman-emperors.html
During the mid and late periods of the empire most emperors were born outside of Italy most famously of Illyrian origin.
The Byzantine empire(East roman empire) was more Greek than Latin so it is understandable that its emperors were not from Italy.