The precise nature of the relationship between the popes and emperors – and between the Papal States and the Empire – is disputed. It was unclear whether the Papal States were a separate realm with the pope as their sovereign ruler, merely a part of the Frankish Empire over which the popes had administrative control, as suggested in the late-9th-century treatise "Libellus de imperatoria potestate in urbe Roma", or whether the Holy Roman Emperors were vicars of the pope (as a sort of Archemperor) ruling Christendom, with the pope directly responsible only for the environs of Rome and spiritual duties.