How did Diocletian’s tetrarchy divide power in the Roman Empire?

Diocletian’s tetrarchy, or "rule of four," was established to manage the vast Roman Empire by sharing power among four leaders, thereby addressing military instability and the difficulty of governing such a large territory from a single center.12

The system functioned as a collegium of emperors divided into two tiers:
* The Augusti: Two senior emperors, Diocletian and Maximian, who held primary decision-making authority.12
* The Caesars: Two junior emperors, Galerius and Constantius I Chlorus, who served in executive roles and were attached to the Augusti.12

While the empire remained an undivided inheritance (patrimonium indivisum), it was administratively partitioned into four sectors of operation, each with its own capital:
* Diocletian (based in Nicomedia): Oversaw the East, including Thrace, Asia, and Egypt.12
* Galerius (based in Sirmium): Oversaw Illyria, the Danubian provinces, and Achaea.12
* Maximian (based in Milan): Oversaw Italy, Sicily, and Africa.12
* Constantius I Chlorus (based in Trier): Oversaw Gaul, Spain, and Britain.12

This structure aimed to stifle usurpations and ensure efficient defense, with the Augusti and Caesars linked by marriage or adoption to maintain unity.12