About 22% of the current Australian population has ancestors who were transported to Australia as convicts. This estimate comes from a project by the genealogy websites www.ancestry.co.uk and www.ancestry.com.au (they looked at more than just the genealogical records, also using demographic data such as birth rates, and census data).

From the earliest British settlement in Australia to about 1850, the number of transported convicts and free settlers were similar. About 162-165,000 convicts (or 163,021, if the number from the study noted above is accurate) were transported to Australia between 1788 and 1868 (when convict transportation stopped). The number of free settlers between 1788 and 1850 was about 200,000. Considering this, 22% might seem quite low - after all, only one convict ancestor is need to be descended from a convict ancestor, and that ancestor could be 10 or more generations back. Thus, one could be of convict descent and only have 1/1,000,000 convict ancestry.

Three things are responsible for that 22% figure being so low. First, only about 15% of transportees were women. Men outnumbered women among the free settlers too, but the imbalance was far smaller than among convicts. The convict and settler population of Australia in 1851 was about 438,000, consisting of 257,000 men and 181,000 women, and the gender imbalance had been greater before then. Natural population growth was limited by the female population, and many of the male early convicts had little chance to leave descendants.

Second, many transportees returned to Britain at the end of their sentences. Since there are about 4 million descendants of convicts transported to Australia in Australia, and 2 million in Britain, the number who returned was significant (but probably less than 1/3 of the total, since male returnees to Britain lived in a more gender-balanced population).

Third, large-scale immigration to Australia began at about the time that transportation of convicts ended (with the discovery of gold in Australia motivating many of the new immigrants in the mid-19th century). As noted above, the population in 1851 was 438,000, and by 1861, it had reached 1.2 million, and by 1881, 2.3 million. It was 3.8 million at Federation in 1901 (i.e., when the various colonies in Australia united as the Commonwealth of Australia). From 1851 to 1891, immigration was approximately equal to natural population growth. This was a great dilution of convicts and their descendants in the Australian population. When immigration slowed at the end of the 19th century, the fraction of Australians with convict ancestors would have increased, so 1891 may have been the time when the fraction of the settler population in Australia of convict origin or ancestry was lowest.

Of course, since Australian residents commit crimes, many Australians are descended from criminals who were not transported convicts. (The same is true in other countries, and including these criminals could easily make the majority of the population of almost all, if not all, countries descended from criminals.)

About 800,000 Australians identify as indigenous Australians; the great majority of them have indigenous ancestors. Many more Australians will have indigenous ancestors, but not identify as indigenous (indeed, many won't know that they have indigenous ancestors). It is possible that more Australians might have indigenous ancestors than convict ancestors. If not, the number will at least be of a similar order of magnitude.