The 'descended from criminals' thing is not really accurate but its short easy and amusing so it has stuck. The true story is far more complex of course.

Firstly, from a genetic viewpoint probably every person in the world is 'descended from a criminal' of some sort. We're far more interconnected than we think. So its hard to be even sure what it even means or whether it has any validity as a viewpoint. IF you have 32 great x grandparents, and one of them was a convict and 31 were not, does that mean you're 'descended from a convict' and what does that imply?

The reason Australia was chosen as a convict colony is because the UKs previous penal dumping ground had recently rebelled and gone solo. So many Americans would also be 'descended from criminals', but this stopped circa 1776.

Australia was founded from a series of colonies that were dotted around its shores. These colonies generally became the center of the States that now exist. There was no absolute guarantee that they would become 'Australia', they could easily have become 7 separate countries. In fact New Zealand was mooted as joining Australia but chose, wisely, to go it alone. These colonies all have seperate stories.

Some states, like Victoria, were founded almost entirely independent of the original penal colonies and thus have little or no connection with them. People migrated there from the UK and from other colonies. But mostly from the UK during the gold rush of the 1850s. Australias population grew from 440,000 to 1.15million in 10 years, the vast majority of the increase was in Victoria.

Western Australia was founded by a group including a small number of convicts and had a grand total of under 10,000 sent there throughout its time, hardly a massive influx.

In total 165,000 convicts were sent to Australia , but as the Gold Rush increase was in itself in the order of 700,000 people in just 10 years then you can see that the term 'descended from Criminals' is far less likely to be as accurate as 'descended from Gold Miners' (even though the crims turned up earlier). Australia has also long had substantial migrant numbers from Europe, with substantial increases after WW2. With a population of only 7 million people in 1945 they have had 6.5 million people migrate to Australia since then. For a total of 23million today.

So overall 165,000 convicts were sent to Aust. in 70 odd years. in the 1850s alone 700,000 new (non convict) migrants turned up and another 6.5 million turned up post 1945. So whereas in the early years a substantial percentage were convicts, these were rapidly drowned out by the millions who started arriving later. One thing people also forget is that the convicts werent dumped on the shore. A substantial number of soldiers and administrators and free persons also arrived to help build and control these colonies.

Most of this was 150-200 years ago. Many generations. Immigration numbers far exceed the number of convicts. No ones 'grandparent' was a convict, perhaps a few have great great grandparents, most would be older than that. New migrants would far exceed those numbers. A percentage is meaningless. I dont know anyone who knows that an ancestor was a convict, most peoples background goes back 3-4 generations then disappears back to Europe. I dont even want to estimate a number, but it would be very low. This is a misunderstood meme that is hard to articulate into meaningful numbers when viewed objectively.