New Guinea is part of Australian continental block. Malaysia is part of Asia. A number of plate boundaries including retroarc basins, spreading centers and subduction zones are in this part of the world where the Indian/Pacific Oceans meet.

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Your question is a very good one and brings up interesting issues about the definition of a continent.The easiest way to think of a continent is as a continuous land mass and its closely associated islands. By this definition, what continent would Malaysia be a part of if its peninsular part is next to Thailand on the Malay Peninsula?

A more difficult question is what continent Indonesia belongs to. If one uses proximity to another continent, Indonesia is very close to both Asia (across the Straits of Malacca -- a very important strait for studying currents and shipping) and Australia (across the Straits of Torres and the Timor Sea -- you might make an exercise of measuring whether it's a longer distance from Indonesia to mainland Australia or from Indonesia to mainland Asia). You might consider Indonesia to be a part of the same continent as Malaysia because Indonesia shares the island of Borneo with the island
parts of Malaysia (the states of Sarawak and Sabah). But Indonesia is also composed of some very large islands and maybe shouldn't be considered a part of a specific continent at all. You may often see that many island nations in the Pacific Ocean are not associated with any continent and are actually lumped together as Oceania. Perhaps because Indonesia isn't connected to Australia or Asia, it should be left unattached.

Ultimately, what continent Indonesia belongs to should depend on why you want to associate it with a continent. For the purposes of determining currents, both the Torres Strait, and the Straits of Malacca are relatively shallow water bodies and Sumatera (Indonesia's western large island) might be geologically considered a part of Asia and Irian Jaya (Indonesia's eastern large island which is shared with Papua New Guinea) might be geologically considered a part of Australia. In this case, I think that the political boundary of Indonesia is not as important as the geologic situation of its various islands. If you are interested in cultural issues, you might note that many of the people of Indonesia are of Asian descent whether they be relatively recent Chinese immigrants or people from parts of Asia that settled in Indonesia several hundreds or thousands of years ago. In the cultural and economic sense, you might find that Indonesia identifies itself much more with Asia. You have brought up very interesting questions in geography that highlight the differences between a physical explanation for whether a given place belongs to one continent or another and a more political perspective where a nation covers many islands (in the case of Indonesia) or exists on both islands and a continent (as in the case of Malaysia) but is unified in a way that doesn't necessarily make sense in terms of the physical setting.