From its founding its has been an institution “of” and “for” its students (the origin of the Colegiatura)

Initially, the Founder appointed two Dominican friars as rector and vice-rector, but reserved the right to appoint the Colegiales, who would enjoy a full scholarship and live in the cloister until graduation for more or less seven years.

The Dominicans, brothers in the Founder's religion, understood the donation of the school in an absolute sense and intended to incorporate it as part of the dominican religious community. Realising this, the Founder then proceeded to revoke the donation and to secularize the College, a process completed by Dr. Cristobal de Araque.

This permitted the continuance in Spanish America of the tradition of Universitas scholarium, in which students form the basis of the institution. A tradition originating in Bolonia, the alma mater of European universities. This structure being distinct from the Universitas magistrorum as followed in Paris. 

The Organizational Model of the Colegio Mayor del Rosario

It is similar to that of a Colegio Mayor in Salamanca (Spain), also called Colegio del Arzobispo and currently Colegio Mayor de Fonseca, which means it is a private and autonomous institution governed by its students. The Colegiales de Numero can be considered similar to the fellows of English colleges, whereby they enjoy full scholarships, elect the university directors, and occupy positions of responsibility in the Claustro.