Robert Hughes wrote an extensive account of the formation and immigration system to Australia. The book is called The Fatal Shore: the epic of Australia's founding. It's an authoritative and detailed account of who was shipped out to Australia during the time when it was a penal colony for British and Irish prisoners. For the most part those sent had committed crimes against property. Stealing was high on this list - even what would be considered nowadays as petty theft like stealing food might result in transportation. Young children caught stealing were also amongst those transported. Some of the Luddites, who broke machinery in protest against automation and the accompanying loss of jobs, were also transported to Australia. The so called Tolpuddle Martyrs, agricultural labourers who attempted to form unions were also transported.

Also on the list were political prisoners. From around 1800 these involved many Irish rebels who rose in rebellion against British rule in Ireland. As Hughes said ''From the outset, the Irish in Australia saw themselves as a doubly colonised people." Transportation to eastern Australia ended in the 1850s when Australian authorities began to object to Britain sending their prisoners. The last ship sent to western Australia in 1868 carried some 60 Irish Fenian prisoners.

According to Hughes the main philosophy behind the notion of transportation came from the idea developed in the late 18th century that British society needed to rid itself of undesirables. That a complete purge of those who didn't 'conform' to society's rules was the only way to weed them out - they could not be reformed, they needed to be banished.

Edit: typos

Hi, FYI you'll find more info in these

• What was the minimum crime in England that was required to send someone to Australia as punishment? featuring /u/CopperBrook

• What were the "19 Crimes" that sent you to Australia featuring /u/Brassafrax

and, of possible tangential interest ...

• Did the transportation of convicts to Australia lower the crime rate in Britain? featuring /r/RTarcher

Thanks for all your help! Both family anecdotes and the sources you recommended​ have helped. And thanks for the highest upvoted post I've ever had.