I think in lay speak it translates as 'having reasonably friendly relations with until the US invades them and then we're not friends with them anymore and will expel their diplomats with less than 24hrs notice'
Yes, until 1975 Australia did occupy PNG, though the word I always remember hearing was the much more lightweight 'administer'. It was a colonial occupation, and since then Australia has given a massive amount of foreign aid to PNG, and offered the services of the Australian Federal Police, tax officers, and other boring bureacratic types to try to assist in overcoming some of PNG's issues. And the relationship isn't the same warm and incredibly fuzzy bro one that it is with NZ...
'Although close relations have been maintained since peaceful independence and Australia remains the largest bilateral aid donor to Papua New Guinea, relations with Australia have recently shown signs of strain. While on a state visit in March 2005, Prime Minister Somare was asked to submit to a security check and remove his shoes upon arriving at the airport in Brisbane. Despite demands from the PNG government that Australia apologize, the latter refused. Additionally, problems have arisen with regard to Australia's latest aid package for the country. Valued at A$760 million, the program was to tackle crime and corruption in PNG by sending 200 Australian police to Port Moresby and installing 40 Australian officials within the national bureaucracy. However, after the first detachment of police arrived, Papua New Guinea's high court ruled that the arrangement was unconstitutional, and the police returned home. A new arrangement, by which only 30 officers will serve as a training force for the local force has been described by the Australian foreign minister as "second-best"
http://en.wikipedia.org/wiki/History_of_Papua_New_Guinea#The_Territory_of_Papua_and_New_GuineaThe relationship between Australia and New Zealand is on a whole different level entirely. When our pollies say the US is our strongest and closest ally, they're talking shit. It's NZ by a mile. There's the historic and cultural similarities for a start. While European settlers in Australia were British, European settlement in NZ came about from those same settlers travelling from Sydney to NZ, so they were basically settled by Australians. The ties between the two countries when it comes to trade and defence are far beyond merely having a close relationship. There's the whole ANZAC thing, which is incredibly strong, and they sound the same as us, except they say 'sex' instead of 'six' which is always a cause for snickering when drinking with a Kiwi. I don't know if the US has a relationship similar to it, but I'd assume that the Scandinavian countries might have a similar thing between themselves....
on edit: Sorry, but I've got the sudden urge to post something from Flight of the Conchords...
http://www.youtube.com/watch?v=f2gii2nenUg