Maximum extent of an empire ruled from Constantinople

Sorry for double posting but i meant this to be posted in pre 1900, please delete the one in post 1900 as it obviously deal with a medieval/early modern technology.

For an empire ruling from Byzantium, what territories can be held long-term and economically integrated into the state? This question assumes pre-industrial technology, but I am also open to speculations about the size of a hypothetical Constantinople empire with telegraph, railways, and steamboats. At what point are new conquests totally economically unviable and better spun off as vassals? Finally, is it possible for a later state (Post Justinian ERE, AH Ummayad, Ottomans) to recreate the interdependent maritime economy of principate Rome?
Consider the following regions, whether they can be economically/politically integrated in the long run:
Yemen
*Mesopotamia
The Caucasus (down to Tabriz)
Don valley
Tunisia and Libya
Further Maghreb
*Naples/Sicily
North Italy
Austria
Hungarian Plains
 
Probably a Byzantine Empire that was able to immediately build upon their success during Justinian's years an essentially reunites all of the old Roman Empire, with the exception of northern Gaul (the Franks are too strong at that point) and distant Britannia.
 
Happened OTL (Ottomans, though not really in the long run)

The Caucasus (down to Tabriz)
Happened OTL, and had the Safavids collapsed the Ottomans would have permanently kept Iranian Azerbaijan.

Don valley
Ottomans could have managed, though probably through Cossack and Tatar vassals more so than direct rule.

Tunisia and Libya
OTL

Further Maghreb
OTL for Algeria. For Morocco, could have happened if the OTL civil war that led to Saadid unification and Moroccan renaissance took a different course.

*Naples/Sicily
Ottomans might have taken parts of southern Italy if Mehmed didn't die in 1481 and the Otranto invasion went really well.

North Italy
Probably impossible for Ottomans as we know them

Probably some sort of vassalage would have been enforced, but the Ottomans could certainly have taken Vienna and eastern Austria.

Hungarian Plains
OTL
 
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