Note that in IVAO we have a system where the higher ATC position takes care of the lower ones, if that/those lower one(s) is/are not occupied and active. Still FRA's (Facility Rating Assignment) do apply!
The sequence (from high to low) is:
CTR (Center)
APP (Approach)
TWR (Tower)
GND (Ground)
DEL (Delivery)
Thus, if only CTR is active within a specific area, he controls ALL of the controlled airspace. That includes the controlled aerodromes there, where he acts as well as APP, TWR, GND and DEL for all of those aerodromes.
If at a controlled aerodrome there is only APP active, than he controls the whole of the aerodrome control area. That is, he acts as well as TWR, GND and DEL for that airfield.