Ok. Now that I am a bit more composed/less tired: what I meant is this. Obviously based on the building and references you have institutional/formal framework for higher education with chairs, professors, lectures, etc. My question is the relationship between that and the "University" as we define it, especially:
1) The qualification/grouping of teachers-how were these institution's staffs defined and was there a formal structure for accrediting, choosing, and compensating teachers, and for determining responsiblities? What non-academic staff existed and how did they relate to the academic staff etc.
2) Students-what defined people as students? Did these institutions have defined bodies of students and a set list of procedures for matriculation and graduation, a register or set of students? What defined one as a student.
I know for example the University of Constantinople or School of Nisibis existed, but I don't know how the organizations worked, if there was a set curriculum, if students simply showed up to lectures or had to register as students, how teachers or staff were chosen, or what lessons or lectures existed. Interestingly enough, Wikipedia (admittedly not a reliable source) suggests that Persia's Jundishapur had something closer to a modern higher education model, with students being instructed under the scrutiny of the hospital's staff as a whole and expected to pass exams to qualify to practice or teach.