No, both are separate universities, although some universities also have satelite campuses (UDeM (montreal) has multiple).
replyEdit0: Although UQ is a group of 10 universities that are public, they are not a single entity.
That sounds like the UC or SUNY systems. UCSB, UCLA, etc are all separate institutions with separate missions, but it’s totally normal to say “UC Berkeley” or “UC Santa Cruz.”
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