I am referring to the definition in the reference given by Peter in the Dbox re institutions that have their degrees awarded by other universities. See here for the UK

https://eacea.ec.europa.eu/national-policies/eurydice/conten...

...publicly funded higher education providers or alternative provider

"Many colleges and other institutions, such as further education colleges, do not have degree awarding powers, but provide complete courses leading to recognised UK degrees. Courses at these institutions are validated by institutions that have degree awarding powers under a formal recognition arrangement. These other providers of higher education programmes may use other institutional titles such as ‘college’. The use of such titles is not regulated by law.

Higher education provision in further education institutions may either receive direct public funding, or be funded via a franchise arrangement. A franchise arrangement, which can cover all or part of a programme, means that a student is registered at a higher education institution, which receives the funding and is responsible for quality assurance. The HEI then passes a proportion of the funding to the further education college providing the teaching.

In cases where 55% of the students at such an institution or college are studying courses of higher education, it may transfer to the higher education sector, becoming a higher education corporation (HEC). The institution will then become eligible to receive direct public funding from the academic year 2019-20 onwards, which it must apply for through registering with the Office for Students (OfS) and meeting its initial and ongoing conditions of registration.

Until 31 March 2019, decisions on applications from institutions wishing to transfer into the higher education sector and be eligible for public funding rested with the Secretary of State, in line with guidance from the Department for Education (DfE).

Alternative providers ..."

--------------------------------------------------
Note added at 9 hrs (2020-11-30 02:13:33 GMT)
--------------------------------------------------

https://es.wikipedia.org/wiki/Centro_Universitario

Centro Universitario es el término utilizado en España para referirse a un centro docente independiente que imparte titulaciones universitarias oficiales en nombre de una universidad, como centro adscrito a esa universidad, pero sin formar parte de ella.

Un ejemplo puede ser un Centro Universitario que imparta la carrera de Derecho adscrito a una universidad oficial. En este caso, el estudiante cursaría las asignaturas en el Centro Universitario, siguiendo el Plan de Estudios de la Universidad Oficial

--------------------------------------------------
Note added at 17 hrs (2020-11-30 10:32:06 GMT)
--------------------------------------------------

Yes, I actually started with "F.E. College" as the heading and meant to put a slash or "OR" when adding the alternative. I'd probably use "third-level colleges/institutions" myself as not all courses in FE colleges lead to the awarding of diplomas or degrees. BUT they certainly do exist and what IS meant here IMHO.
When I was doing my first BA I could have simultaneously taken an LL.B in another institution, to be awarded by my university. (Wish I'd done so but I was a rather lazy 19-year-old!)
So legal, accountancy, MBE, teacher-training etc. courses are often studied in other institutions with degrees, diplomas awarded by affiliated universities.

--------------------------------------------------
Note added at 17 hrs (2020-11-30 10:33:48 GMT)
--------------------------------------------------

third-level colleges/institutions OR Further Education colleges

--------------------------------------------------
Note added at 17 hrs (2020-11-30 10:35:13 GMT)
--------------------------------------------------

BTW I have never seen this as "university centre"

--------------------------------------------------
Note added at 4 days (2020-12-04 11:35:10 GMT) Post-grading
--------------------------------------------------

Glad to have helped.
I see you are using a variety of terms but I think third-level/Higher Education colleges/institutions basically act as umbrella terms. And yes, affiliated to the degree-awarding university.