There is no clear official definition of what was a studium generale. The term studium generale first appeared at the beginning of the 13th century, out of customary usage, and simply meant a place where students from everywhere were welcome, not merely those of the local district or region.
In the 13th century, the term gradually acquired a more precise (but still unofficial) meaning as a place that (1) received students from all places, (2) taught the arts and had at least one of the higher faculties (that is, theology, law or medicine) and (3) that a significant part of the teaching was done by masters.
A fourth criterion slowly appeared: a master who had taught and was registered in the Guild of Masters of a Studium Generale was entitled to teach in any other studium without further examination. That privilege, known as jus ubique docendi, was, by custom, reserved only to the masters of the three oldest universities: Salerno, Bologna and Paris. Their reputations were so great that their graduates and teachers were welcome to teach in all other studia, but they accepted no outside teachers without an examination.
That lock was picked by Pope Gregory IX, who, seeking to elevate the prestige of the papal-sponsored University of Toulouse, which he had founded in 1229, issued a bull in 1233, allowing Masters of Toulouse to teach in any studium without an examination. It consequently became customary for studia generalia, eager to elevate themselves, to apply for similar bulls. The older universities at first disdained requesting such privileges themselves, feeling their reputation was sufficient. However, Bologna and Paris eventually stooped down to apply for them too, receiving their papal bulls in 1292.
Arguably, the most coveted feature of the papal bulls was the special exemption, instituted by Pope Honorius III in 1219, which allowed teachers and students to continue reaping the fruits of any clerical benefices they might have elsewhere. That dispensed them from the residency requirements set out in Canon Law. As this privilege was granted only to those in studia generalia, certainly routinely by the 14th century, it began to be considered by many to be not only another (fifth) criterion but the definition of a studium generale" . (Although the old universities of Oxford and Padua, which resisted asking for a papal bull, had sufficient reputation to be referred to as studium generale without a bull, Oxford masters were not allowed to teach in Paris without examination. Oxford reciprocated by demanding examinations from Paris masters and ignoring the papal privileges Paris enjoyed.)