AHC: Longest Plausible Gallic and Palmyrene Empires

I don't know about the Gallic Empire, but I don't see why the Palmyrenes couldn't last for several centuries. A Christian Arab empire... might be interesting, especially if they can take down the Sassanids.
 
Well, the Palymernian have better odds to survive. Not only he had some legitimacy to act "roman", as their leaders have been named "Dux Oriens" by the emperor (Dux Oriens is roughly co-emperor), of course before they try to annex all the Asia.

With Zenobia and the conquest of Egypt, it means that wheat (and other cereals) but also luxury products and their trade routes would be blocked for the roman trading class, and it would make a good pressure enough for any emperor worried about please to Rome's upper class to crush the queen. Make Palmyre renounce to control Egypt, and Rome could tolerate it as a vice-kingdom.

Of course it would need an important and continuous pressure in the european limes to force Rome to tolerate a autonomous or independent zone in Syria.

For the Gallic Empire, it's far more difficult. It wasn't created from an existing client state as Palmyre, it wasn't fully supported by the locals and even by the gallo-roman, hispano-roman and britanno-roman elites. (You can see that Tetricus hardly managed to keep only Gaul and somewhat Britain).
Furthermore it managed to exist because of an interest's convergence : the population wanted protection from the Barbarians while Rome not wanted or couldn't give any real help, and the Rhine's legions wanting more acknowledgment of their situation and willing to gain more (even at the cost of local plundering).

Finally both the Roman return to Gaul plus the anarchic militarocracy would have help to crush the Gallic Empire, that never considered himself as different or even distinct from Rome : it was only "we're the romans of Gaul and will defend the province if Rome don't want to"
 
If the Palmyrene realm can stabilize itself while Rome in the west reintegrates, I'd think they'd prevent or limit the Empire's shift of center of gravity eastward. OTL Constantine eventually established his new and major capital at Constantinople, but if much of the reason for his doing so were mooted because Rome did not control the rich eastern provinces anyway, perhaps either the capital remains at Rome itself, or at least a new one is established not so far east, so the defense against invasion more effectively covers the west as well.

Bottom line--by pre-emptively splitting off a crucial part of the OTL Eastern Empire, might the division of the rest of the Empire be prevented?

Frankly I doubt it because first of all the Romans would be pretty obsessed with reconquering Palmyra, and unless the Palmyrines were able to actually seize control of Antatolia and central Greece as well, I suspect that "Rome" would have shifted East just as inexorably as OTL; after all capitals were often moved as much to present a strong front in wartime (with Emperors mainly preoccupied with waging the war, they needed to be resident near the front) as to occupy the center of the source of wealth. Worse, I suppose that by the time the Empire split and left the Western Empire to rot, the Imperial society as a whole was losing both means and will to defend the western reaches; trying to force the center of gravity west might or might not cause a reevaluation of what was vital, but might by no means provide any more resources to try harder with!
 
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