An oft-pondered What-If when AH comes up in academic media is the possibility of Xerxes defeating the Greeks and Greece being incorporated into the Persian Empire. Additionally, in OTL the Persians briefly held Egypt and even Cyrenaica.
My question is how much of Europe and North Africa do you think could realistically be administered as part of a unitary Persian empire? (I.e. puppet states and vassals don't count). I don't mean an empire to last forever, of course, but one with a reasonable lifetime, say a couple of hundred years--an empire that holds those parts of Europe and Africa long enough to put down some linguistic, cultural and government-style roots.
Could the Persians rule over the modern areas of Italy, Tunisia, Algeria? What about the Balkans?