Why did all the convicts start a new life in Australia?

It's not correct to say that all or even "all the" convicts who were sent to Australia started a new life there. Many returned to Britain after serving their sentences, especially the ones sentenced to short terms. Others lived out their days in the penal colonies but did not necessarily adopt a whole new way of life. However, some convicts did indeed make Australia their adopted home, integrating into society through means such as becoming landowners or marrying into the free settler community. Reasons for wanting to start a new life could include seeking opportunities not available to them as former criminals in Britain, the lure of land ownership in some cases, escaping their past as convicts once released, and in due course their descendants simply having no reason to want to leave Australia, since for them it was as much their nation as Britain was now to people there after many generations of settlement on that continent.