WI: theodosius I only had one living son

But this son is the most compent Roman emperor since Trajan. This alt arcadius (because he is the same age as arcadius when his father dies) inherits the whole empire and only has one ambition in life to keep the empire under one ruler and and too let the imprial borders shrink no further. Is that posible and are there any time lines based on this concept?
 
I doubt you'd have a maintained unified imperium : at this point, it was largely accepted that it had to be shared, particularily between West and East.

Remember that Theodosius' unification was more or less accidental, and in any case short-lived : no more than 4 months.

Giving the growingly more important military function of the imperialship, a division will be likely to happen ITTL as well, even if Arcadius is the sole heir of Theodosius (I'd expect him to be Emperor in the East, as he was already junior EREmperor before Theodosius' death IOTL).
Who would be in charge of the west is anybody's guess : I'd think, tough, that some people as Nebridius (which is largely unknown, safe he was a nephew by alliance of Theodosius) or the childs of Thermantia may have a better chance in spite of their relation with Magnus Maximus.

Eventually, if Pulcheria survives childhood, her spouse will be well placed.
 
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