We used to send them your way. Just be glad you went your own way and left Jolly George behind. We had to find somewhere else to send them before the jails burst their seams. Someone had a sparkler of an idea after our man Cook laid claim to Van Diemen's Land on behalf of the crown. We sent shiploads of not only convicts but settlers as well. Troopers, Redcoats and a raft of legal administrators went with them, plus their families. The relationship of legal settlers and 'minders' to convicts was probably at least five-to-one. It had to be. The settlers, or squatters, paved the way beyond the Blue Mountains on the western edge of the colony. Pioneers like Edmund Burke pushed the bounds, out into the central desert area and a new generation of migrants followed after the discovery of gold, opals and other minerals.
Not all convicts were vagabonds and thieves, either. Some were found guilty of organising labour in England, such as the Tolpuddle Martyrs from Dorset who tried to gain rights for farm labourers. Some came back, more never saw England again.
So that's the make-up of Oz. If your great-great grandad was a 'lag' (slang for convict), he was in a sizeable minority, but by no means representative of the country. Many in the last 50 years went to escape unemployment here, as some I went to school with... Such as Bryn Carman, now a self-made millionaire as a result of his pastime, sea angling. Many others escaped the carnage in the Balkans in the 1980s.