It is estimated that about 22 per cent of living Australians had a convict ancestor. Based on Ancestry.com's collection of Australian convicts records.

http://corporate.ancestry.com/press/press-releases/2007/07/ancestry.com-launches-largest-online-collection-of-records-documenting-australias-convicted-founding-fathers/

I'd like to remind posters that personal anecdotes are not acceptable answers on /r/askhistorians.