From the
Air Services Act 1995:
Australian‑administered airspace means:
(a) the airspace over Australian territory; and
…
Australian territory means:
(a) the territory of Australia and of every external Territory; and
(b) the territorial sea of Australia and of every external Territory; and
(c) the air space over any such territory or sea.
Therefore, according to the Parliament, the NLK problem belongeth Airservices.
However, this doesn't answer the question as to who is responsible for providing what services to whom
outside Australian-administered airspace.