I've always just assumed (perhaps incorrectly) that those who completed their sentences settled in Australia, with some even given parcels of land from the government.
followup question: was there such a system in place that did award parcels of land in Australia for those who completed their sentences, or some other similar reward system?
Once a convict completed his/her sentence in full (including the ticket-of-leave period) there was no requirement to remain in the colony. If he could raise the money for fare, or sign on a ship as crew he was free to leave. Some went to America, where part of San Francisco was referred to as "Sydney-Town", later "The Barbary Coast" and were for a while notorious as gangsters called the "Sydney Ducks" in California. America was something of a dumping ground for Australia, the notorious bushranger, Frank Gardiner (not a transportee, as he came out a free settler) obtained early release from prison on condition of exile to San Francisco.
There don't seem to be any studies on convicts who returned to Britain legally after completing their sentence. It would have been very much an ad hoc arrangement as while legal, they would have had to arrange it themselves and would have had no requirement to report anywhere on arriving in Britain.