As far as I know, I have no convict ancestry (unfortunately) despite my own (and my children's) earliest (known) ancestors having come here in 1841, some having come ca 1850 and none later than 1890. I'm still hoping! The closest is a GggUncle on my children's paternal side who was sentenced to 7 years transportation in 1848 for forgery and uttering - but was pardoned before he set sail (and just a few years later came free and became a successful businessman!) And, as far as I know, there is only one on either side who married a convict (again, this is on my children's paternal side! - their Gggma); of her three relationships/marriages, the first (a marriage) was with an ex-con, the second (not a marriage and my children's line of descent) was with a chap who doesn't seem to have been a convict, and her third (a marriage) was with an ex-convict but she was past child-bearing age.
I recall that my late mother was always very keen to show the passage certificates of one set of her maternal ancestors (who came in 1850) to prove that they weren't convicts.
I guess the Australian Bureau of Statistics would be able to put some limits on the percentage? First step would be to discount the % of the current population born overseas (not precise of course - after all, one of my children was born overseas) but at least a rough estimate. And comparisons of this with similar % in earlier censuses.
I guess that, the further back one can trace one's ancestors in Australia, the more likely it is that there will be some convict connexions.
Family lore had it that Henry HACKING of the 1st Fleet was connected - he married a convict but (unfortunately) he's definitely not an ancestor.
Bellejazz, it's a very interesting question and I hope you get some good answers.
JAP