Hi Rod
It depends, if the property is being used by a registered PBI or charity purely as an administration building then it will be COMNV. However if jointly operated for retail or exclusively as a retail store then PUBLIC.
Yes, a University is not a statutory body representing the crown. It is important to remember that state infrastructure is exempt as GOVT purely because of efficiencies in making payments. If a public school was to pay the ESPL Treasury would need to make an equal expenditure offset representing the amounts paid to each public school and councils would be required to bill, transfer and reconcile payments made each quarter.
I trust this information is helpful.
Regards,
Andrew