Who you feel you close too is not important.

The prevailing view, known as the "Out of Africa" theory, holds that modern humans evolved from a common Homo erectus ancestor in Africa. Homo sapiens then left Africa and spread across the world, displacing other hominid species such as Neanderthals.

The competing theory, called "regional continuity," contends that Homo erectus came out of Africa and modern humans evolved from Homo erectus in several different places - what are now Africa, Europe and Asia - with interbreeding between the regions.
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Aborigines arrived in Australia between 120,000 and 50,000 years ago.
(some evidence, particularly changes in pollen counts, changes in the fire regime etc suggests the earlier date. Actual "hard" site evidence (artefacts, bones etc) is only available back to the later date.). There is little doubt that they arrived through New Guinea (which has, on occasion been connected to Australia during the period concerned) from south east asia. It is also thought probable that further groups entered Australia from the north during the following tens of millenia.

New Zealand, however, only appears to have been populated by humans for about 700 years. The Maori's who are Polynesians, arrived around 1300AD. Any genealogical inter-relationships between the Maoris who arrived in New Zealand and the Australian Aborigines, probably pre-dates the original occupation of Australia. The relationship bewteen Aborigines and the population of New Guinea is probably much more recent (trade occured between Aboriginal people of Cape York and the Torres Strait Islands prior to white contact, and asociations between Aborigines on the Arnhem land coast and people from Indonesia etc are well documented).