The Aus FIR (Flight Information Region) extends a bit over halfway to NZ. This is well out of radar and VHF range, as most of Australia itself is.
ATC in non-radar airspace is maintained through position reporting via HF (radio), CPDLC (texting) and ADS-B (GPS).
An aircraft may still be in Aus airspace, but due to unfavourable communication conditions, be controlled via relay through NZ ATC, and vice versa.
Aus ATC is part of a network of units in surrounding FIRs, Primary Guard being given to that unit which may maintain the most effective comms with the aircraft. As in the above example, this means that an aircraft in South African airspace may still be controlled via relay through Aus ATC if conditions merit it.