Quoting from the same link the support for my claim that Britain also transported the convicts to Australia:

https://en.wikipedia.org/wiki/Convicts_in_Australia

"Between 1788 and 1868, approximately 162,000 convicts were transported to the various Australian penal colonies by the government.[1]

The British government began transporting criminals to overseas colonies in the 16th century. When transportation to the American colonies declined with the move towards American independence in the 1770s, an alternative site was needed to avoid further overcrowding of British prisons and hulks. "