Practically none for what matter western Romania : these men were invested (or, more often than not, invested themselves) in the late Empire with administrative (
militia) roles would it be military (Vicentius was probably trusted the military charge of Taraconnensis by Majorian) or civil (which was generally translated by an episcopalian position, but not always).
Most of them joined up Barbarians, as part of their kingoms' militiae, because the fall of the Roman state in West only let Barbarian imperium as a legitim authority coming from imperial institutions. Similarily, Barbarians rulers readily accepted them as part of their military and administrations, because not only it strengthened their own power (the death of Vicentius was a blunder for Euric's power in Spain, for exemple), but it strenghtened their role as successors of the empire.
Some of these, however, as Burdunellus, Sidonius (for a time) or Syagrius did, tried to assert their power independently, or rather in opppsition to Barbarians, but they were no real difference in matter of power and network between Burdunellus and Vicentius, for exemple : only the latter elected (with the main part of late Roman militia and elites) to serve the Romano-Barbarian state, which succeeded to the western Roman state.
As long you're in a situation where Barbarians are the legal and institutional successors of the roman state in the west, and acknowledged as so by Constantinople and post-imperial Roman militia and elites, it won't be anything more than a ponctual and regional outburst.
(Now, in another discussion thread,
the possibility of a more or less romanized ensemble of high-kingships in sub-Roman Britain was put forth, especially because the situation was more chaotic than it was in Gaul or Spain)
For what matter the post-Justinian reconquests in Africa and Italy, it's a bit more complex.
It was generally less a claim to forge their own states, but to dispute the imperium to whoever ruled in Constantinople (as for Gregorius or Eleutherius, or more obviously with Heraclius), or more of a munity as in the case of Stotzas for exemple. For every usurpation that managed to chase off a previous dynasty, you had a lot of failed and abortive rebellions such as Magnum listed : they didn't formed rump states because not only they didn't tried, but because they couldn't if the imperial claim failed.
Not that you didn't have few genuine tentatives to carve out of the empire some independent (probably more de facto than de jure, tough : exarchates were growingly independent since Justinian, especially Carthage) entities, as Mauricius' ducal claims, but they failed mostly for the same reasons.
That said, I don't see why exarchates couldn't eventually be percieved as their own states, more or less subservient to Constantinople : in a no-Islam TL, for exemple, the aformentioned growing autonomy (and neglect, Africa is barely mentioned in imperial archives after the VIth) of the Exarchate of Carthage (and, a bit less so, the Exarchate of Ravenna and the Roman Duchy) couldn't lead to de facto post-imperial states.
But for what matter the Vth century, I don't see it happening without a severe decline, if not partial collapse, of the eastern Roman state