what is its transition to empire like?
The political and military upheavals of  the 1st century BC transformed the republic to an empire.
Roman Empire
. For various reasons, the 1st century BC was a time of political and military upheaval, which ultimately led to rule by emperors. 
what was the capitol of the roman empire The city of Rome.
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Roman Empire [SEP] Transition from Republic to Empire
Though the old constitutional machinery remained in place, Augustus came to predominate it. Although the republic stood in name, contemporaries of Augustus knew it was just a veil and that Augustus had all meaningful authority in Rome. Since his rule ended a century of civil wars and began an unprecedented period of peace and prosperity, he was so loved that he came to hold the power of a monarch "de facto" if not "de jure". During the years of his rule, a new constitutional order emerged (in part organically and in part by design), so that, upon his death, this new constitutional order operated as before when Tiberius was accepted as the new emperor.