Good Lord, have we stopped shipping miscreants and undesirables out to Oz ? I was thinking of putting in a request to have that nauseating Piers Morgan banished to the colonies. The Yanks have just returned him marked 'unwelcome', and they'll put up with anything.
5th generation (family originally from northern Italy via England)
The comments about hoping for a convict in the family tree reminds me of an article I read in a women's magazine some years go. Be careful what you wish for. I imagine stealing a loaf of bread or some other minor transgression is OK to mention re family history, however the person interviewed in the article said she had traced a client's family back to a convict with an offence it might be better NOT to mention. The convict was transported...for having sex with a sheep. 
My ancestors arrived much later (thank goodness) looking for gold.
It must be rare that anyone can say this nowadays.
But I knew the daughter of one of our original convicts, a man called Edward Anquetil.
And I am not all that ancient either.
His daughter was my great grandmother & she was pretty old when I knew her, I was about 6.
Her convict father had been a couple of decades older than her mother. He was transported in 1846 at the age of 15 & he kept his convict past a bit of a secret, I only discovered it a couple of years back.
So about 5 generations back to 1842, though I am a new grandmother so my grandchildren will be 7th generation.
On the other hand, my mother's dad was a migrant, and her mother's family hadn't been here long either.
