I second to that. I would do things that would coincide with the character's traits. Other stuff are based on historical common sense.
For RP purposes, I also make the new basileus stop whatever he's doing and run back to the capital (with his army in tow...heh heh) to 'solidify' his claim to the title. If he's in the middle of a campaign then it makes the pacing of the campaign a lot more fun...
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