My last aeroplane purchased from the US came with an Aircraft Bill of Sale via US Department of Transportation and Federal Aviation Administration. This was needed for Australian Customs as well as disposal by the previous owner.
The FAA and the previous owner and myself have a copy.
I also have a bank copy of cash transfer in US funds.
I would use this to test a case of legal ownership in Australia, as would I expect with any subsequent sale to another owner who could rely on my signature on a registered and witnessed Bill of Sale in Australia stating the aircraft is unencumbered.
The next purchaser would have to satisfy himself of any caveat emptor issues that may arise as a subsequence.
CASA detail the Registered Owner, The Registered Operator or the Registered Owner/ Operator. I suppose this with the above Bill of Sale etc would be a reasonable test of ownership.
But I'm not a Lawyer!