Short answers, pulled from the story.
Roman emperor Diocletian instituted the Tetrarchy in 285 to address severe military and administrative crises. The formal tetrarchic structure began in March 293 when Galerius and Constantius were appointed caesares under their respective augusti.
Nicomedia became the capital of Diocletian, Sirmium was the capital of Galerius, Mediolanum served as the capital of Maximian, and Augusta Treverorum was the capital of Constantius. Aquileia and Eboracum also functioned as significant centers for Maximian and Constantius respectively.
The tetrarchic system lasted between AD 293 and 324 though its effective stability ended much earlier. The period saw mutually destructive civil wars eliminate most claimants to power by circa 324 when Licinius resigned after losing the Battle of Chrysopolis.
Diocletian created this structure to ensure that an emperor could personally command troops on multiple fronts simultaneously. This solved a critical problem from the Third Century Crisis where leaders were often unable to be in more than one place at once.
Constantine defeated Maxentius at the Battle of the Milvian Bridge in 312 leaving him in control of the western part of the empire. The system effectively collapsed by 324 when Licinius lost the Battle of Chrysopolis leaving Constantine in control of the entire empire.