How is the story with the bottom half of the country and the jets coming from nz/USA etc is that also procedural like tops or radar?
The radar coverage in Aus is quite limited, the coverage is mostly limited to what we call the j-curve which basically gives radar coverage in an area from Adelaide around to Brisbane covering most of tassie at high levels. There is also some coverage about 250nm around Perth.
So basically traffic that stays on the east coast usually stays within radar coverage depending on level.
The rest of the country is mostly procedural, with more and more ADS-b appearing as aircraft become equipped and the last of the sites are being turned on. Eventually ADS-b will give the ability to provide radar like separation across most of the country.
For those of you who are unaware what ADS-b is take a look at this link.
Automatic Dependent Surveillance Broadcast (ADS-B) - Airservices Australia
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.
The relaying of comms generally does not involve the ATCO's, in Aus all HF comms for international aircraft are handled by Flightwatch International based in Brisbane. An aircraft in australia's airspace may be talking to a South African HF operator or vice-versa. The control of the aircraft is the sole responsibility of the ATCO that is responsible for the airspace the aircraft is in.