While there were multiple splits in the Roman empire, only one lasted which was the split in 330 AD, which created the eastern and western Roman empires.
What if this split never occurred?
This is an inaccurate portrayal of the various administrative divisions of the Empire. First of all, there's nothing about AD 330 that has anything to do with the division of the Empire. The only thing that happened that year was the dedication of the city of Constantinople as the New Rome. Thats certainly big, but the Empire was unified until the death of Constantine 7 years later, and he divided the Empire in almost Frankish fashion, in 4 different parts.
The fact is that the division of the Empire was almost always done on an ad hoc basis, just to handle whatever current challenge the Empire was facing. The only real de jure attempt to divide it was Diocletian's tetrarchy, and even that was haphazard. Plus, no-one was ever in doubt that Diocletian was the First Among Equals, so that helped. Maximian was going to take his orders from Diocletian, and everyone knew it. Even if they were nominally the same rank.
Whenever there was a particularly capable Emperor, or the exterior threats to the Empire seemed to be waning, the Roman state almost inevitably reverted to a sole ruler.