Building on the work of his predecessor, Julia Gillard, Abbott got down to business with Li on their "strategic dialogue" and deepening what were already the closest ties that the People's Liberation Army had with any Western military. Abbott made a crucial concession to lower investment barriers - which he previously said he'd raise - which took them much closer to closing a free trade deal after nearly a decade of bogged negotiations.

Most strikingly, reflecting the rapport established in the search for MH370 and several years of concerted Australian strategy, the two sides have agreed that the PLA Navy will operate under the command and control of Australia, under the overall direction of the United States, when China for the first time joins more than 20 other nations in the "Rim of the Pacific" naval exercises to be held off Hawaii in July.

When Li finally got around to mentioning China's "core interests" - the dreaded code for everything that Beijing from time to time vents its fury about - he did so only in passing, towards the end of the meeting, without reference to any of the strategic flashpoints that had erupted in Abbott's first few months in charge. At that point Abbott could afford a deep exhalation of breath, and so too could his mentors, because the dire predictions about him running aground in China had not come to pass. "Tony is doing a very good job," said former prime minister John Howard.

It has become a rite of passage for Australian prime ministers to negotiate security and economic contradictions presented by rising China. Abbott, with his stated commitment to "Anglophone" values, was never going to disappoint.

"Howard's visit to China in '97 was a lot like Abbott's," said Ric Smith, Australia's ambassador to Beijing at the time. "Howard went there with baggage, like Abbott, in fact with more than Abbott. He developed this dual narrative that China was a tremendously important country and we respect what they've achieved, but there were differences in history and culture. Abbott has echoed all of this but he's doing something that Howard didn't: Abbott keeps talking about values."

Over the course of Howard's term, China rose from buying 2 per cent of Australia's export shipments to being Australia's second most important trading partner. Its share of exports had risen to 14 per cent when Kevin Rudd's towering ambitions collided with a perfect storm of challenges beginning with the arrest of Stern Hu and ending with the chaos of Rudd's office. Now, China's share of Australian merchandise exports has grown to a staggering 36 per cent, according to the latest monthly data

compiled by Westpac's Robert Rennie. And China has emerged from ''biding its time'' to shaking the strategic equilibrium of the world.

When Abbott came to power he immediately responded to China's muscular advances over its maritime perimeter - oceans that carry as much as 65 per cent of Australia's export shipments - by siding closer to Japan. In November he instructed officials to publicly protest China's ''coercive'' declaration of an Air Defence Identification Zone over a vast area administered mainly by Japan. China backed its new claim with threats of ''emergency defensive measures''.

In early December China's top foreign affairs official excoriated Foreign Affairs Minister Julie Bishop, with cameras rolling. Days earlier, ultimatums had been delivered by senior serving and retired Chinese officials at a forum this reporter attended in Canberra behind closed doors. They were layered like a symphony - and laced with occasional humour and references to Colleen McCullough, Patrick White and Crocodile Dundee - but rarely has there been such a pointed articulation of what the Australian National University defence strategist Hugh White calls ''the China choice''.

Australia could no longer ''rely on the economy of one country and security of another'', said an official. ''You must avoid getting into a corner you can't get out of,'' said another. ''If you don't have China in future then your whole prosperity will be affected,'' said a third.

These are the propositions Abbott set out to test this week. Abbott arrived in Tokyo on Sunday having jettisoned his references to Japan as a ''strong ally'' and Australia's ''best friend in Asia'' which, after all, even Japan's appreciative leaders could not easily reciprocate. Gone also were his government's attempts to uphold American economic primacy at a time when the US share of Australia's merchandise exports had fallen to one-tenth of China's, according to Rennie. But his underlying calculus of security and values had not changed. In Abbott's reckoning, spelt out in interviews with Japanese newspapers, Japan deserved and needed to escape the constraints of its pacifist constitution.

Abbott and Prime Minister Shinzo Abe signed a free trade agreement which fell short of free trade but was nevertheless as good as Australia could hope to get, said former Labor trade minister Craig Emerson. Abe invited Abbott to be the first foreign leader to address Japan's new National Security Council. Abbott thanked his hosts for treating him like ''family'', the Asahi Shimbun reported, and signed a military technology development agreement that a Japanese official said conveyed that Japan would ''aggressively promote defence co-operation with its allies''.

Members of the Abbott team say he and Abe were strikingly at ease and enjoyed each other's company. In Abbott's view, Abe's grandfather, Nobusuke Kishi, was the Japanese prime minister who had bravely opened the iron ore trade with Robert Menzies in 1957. For the leaders Abbott would meet on his next two stops, however, Kishi was the cabinet minister in charge of Japan's war-era industrial machine.

Abbott had expected China's displeasure but not the fury from South Korea. President Park Geun-hye deplored the Abe administration's nationalistic amnesia over World War II and particularly the conscription of Korean ''comfort women''. Her politics are defined, in part, in juxtaposition with her presidential father, Park Chung-hee, who once served the Japanese Imperial Army. If Abbott's support for Abe's Japan was not recalibrated, her ambassador had warned behind closed doors, years of efforts to build defence links with Seoul could not continue.

But if Park loathes Abe's politics, she lives in ever-present fear of her northern neighbour, Kim Jung-un, whose grandfather Kim Il-sung had arranged the assassination of her mother. Abbott and Park found their common interests overshadowed their differences.

''On the South Korean side we have freedom, we have justice, we have democracy,'' said Abbott, after returning from the traditional prime ministerial tour of the 38th parallel and honouring the Australian soldiers who died defending it. ''On the North Korean side, we have an outlaw state which is a threat to world peace and a deadly danger to the people of South Korea.''

Abbott and Park signed an ambitious free trade agreement and resolved to continue tightening military ties - but not without a dig at his predecessor, Gillard, who had set up both.

Next stop was Sanya, China's gateway to the South China Sea, where China's ''aggressive'' military growth and unfounded territorial claims were stoking a ''witches' brew'' for a naval stand-off, the commander of the US Pacific Fleet, Admiral Harry Harris, said in Canberra on the same day.

Naturally, many Australian commentators say the US is pulling Abbott to ''take sides'' against China in its dangerous maritime confrontations. In reality, successive Australian prime ministers have not required American prompting. Nor have leaders closer to the action, most notably in Manila and Hanoi. ''Intimidation must be challenged although it has become clear that this behaviour has done more to enhance the US position than anything the US itself could do,'' said Stefan Halper, director of American studies at the University of Cambridge.

On Friday night, Abbott was to cap his successful odyssey through the geopolitical, historical and dynastic cleavages of north-east Asia with a relatively intimate dinner with the Chinese President, Xi Jinping. Xi's father, as a founder of ''New China'', had fought and feuded with and against the families that control the Koreas and Japan. Those epic differences were set aside, no doubt, as he conveyed news that ''probably the most difficult search in human history'' was drawing to a close because the black box of MH370 would soon be found.

For Abbott's differences in style, emphasis and ambition, the underlying strategy of Howard, Rudd and Gillard remains unchanged. The strategy is to engage with China wherever possible and tighten links with its neighbours and with Washington in case everything goes wrong. Abbott gambled that he could ignore the torrent of warnings that he must start making hard choices between Australia's reliance on the Chinese economy and dependence on the American security umbrella. It's early days but, after his first major test, critics cannot say they have proved him wrong.