The obvious question to ask here is what provincial centers and when? The first Roman provinces were secured in the third century BC, and provincial administration lasted through to the Roman retreat to Italy and the east--if we consider the Byzantine possessions still a part of the Roman provincial system then the scope of the question extends even further. Unsurprisingly, the organization of provinces and their capitals varied a great deal over that time and according to individual provinces.

A few things can be said. Generally speaking as the Roman state absorbed cities and their territory and integrated them into their provincial structure they did not have a general scheme of provincial organization, though one eventually developed over time. When the Romans took over Sicily in 241 they had little idea of how to administer their new territory, and it was not until 227 that two provincial praetorships were formed and appointed to Sicily and Sardinia, on which pattern an additional two provincial praetorships were created in Spain. By the first century a somewhat more regular system of administration, eventually involving provincial promagistrates following Sulla (and legally codified by a lex Pompeia in 53), had emerged, but it would not be until the Augustan and later reorganizations of provincial divisions and seats that the provinces began to follow the same basic models. Provincial capitals did not always make sense, at least not if we consider the purpose of a provincial seat to to the establishment of an efficient administration. This is not quite so. Like Italy, although not nearly so complex, provinces included complex networks of tributary subject-cities, allied cities of various kinds, and free cities. Native cities, no matter what their precise relationship to Rome or the provincial governor, were responsible for the bulk of their own activity, which meant that much of the provincial administration was decentralized from the provincial seat. In any case, during the Republic and well into the Principate the province's "administration," as far as the Roman state was concerned, was the physical person of the governor and whatever personal staff he had about him at any time. As such, provincial seats were not always, at least originally, placed in cities that would lead to the most efficient administration. Africa's provincial seat was at Utica, a reward for the city's defection to the Roman side in the Third Punic War. Even after Carthage was rebuilt by Caesar it was not until around 40 that it became the seat of Africa nova, the African province having been split in two. Sicily, on the other hand, had a bizarre split administration, with a praetor residing at Syracuse but two quaestors at Syracuse and Lilybaeum, despite their resistance to Roman entry into the island and their reduction to the status of civitates censoriae (and the associated transfer of their land to ager publicus). Augustus reorganized the province as the seat of a single proconsular governor and refounded many cities as colonies, but presumably the original motive for seating the provincial administrators at Lilybaeum and Syracuse was at least in part due to their status as conquered territory. These rather complex systems of administration, which established administrative seats not always for the right reasons, were eventually found to be inadequate as central control over the provinces became strained. Diocletian's provincial reorganization established large dioceses and smaller provinces within them, each with their own administrative centers, chosen either for their size and importance to the area or for the convenience of their location--for similar reasons cities like Lugdunum eventually became large cities in their own right.