From his output, ASPI’s Anthony Bergin likes nothing if not to test ideas in relation to Australia’s strategic positioning. His recent proposition that Australia is not so much a ‘middle power’ but a ‘pivotal power’ is a case in point . http://www.aspistrategist.org.au/is-australia-a-pivotal-power/ 
Bergin’s argument is that the common strategic descriptor for Australia as a ‘middle power’ does not accurately reflect its military size or capability, the size of its economy or its strategic reach. In each of these he is correct.
However, the term ‘pivotal power’ is complex. One understanding has it meaning more than just being relatively strategically strong. Indeed, Oxford Analytica defines it not as a quantitative assessment of strategic power but as being a geographic arbiter.http://www.oxan.com/analysis/dailybrief/pivotalpowers/default.aspx
Australia relative to Turkey, as Bergin notes, classifies them both as middle powers. But Turkey’s role with its neighbours, particularly Syria, Iraq and Israel, also mark it as a key regional actor and it is, thus, also considered to be a pivotal power. Closer to home, Indonesia occupies an arbitrating role in the ASEAN regions as well as in relations with Timor-Leste and Australia.
By comparison, Australia is a regional strategic power in the Southwest Pacific, but perhaps less so than it has been. In part this is due to the increasing sense of independence of some of the Pacific island states. In part it is also due to the more active soft power role being played by China in the region, which in turn buttresses this sense of independence – at least from Australia.
Timor-Leste, though geographically close to Australia and a major recipient of Australian aid and, at times, military assistance, has carved an increasingly independent path. If one can define Timor-Leste’s foreign policy, it is one of having a number of strong friends, so that it remains cosseted by some should relations with one turn sour.
Australia’s status in Timor-Leste has diminished, while that of Indonesia has increased. Timor-Leste’s police now train with Indonesian police, and there is an agreement that their armed forces also train together. Australia provides training to, but it does not train with, Timor-Leste’s defence force.
Australia’s strategic status is, on balance, perhaps slightly stronger, or perceived as such, than it has been, given its active participation in recent multilateral conflicts and as a preferred site for training by regional military officers. In another sense, in a strategic environment always in a state of flux, the precise status of any state will remain variable and, more to the point, interpretable.
But if Australia was to suddenly disappear from the strategic stage, the question is the extent to which it might matter. Bergin may be correct and Australia is indeed a pivotal state, if in its own peculiar way.