Apparently a convict gaol was established on Cockatoo Island in 1839 due to the overcrowding on Norfolk Island. Convicts were actually transferred down from Norfolk Island, so ironically some PJ convicts sent north actually ended up back in Sydney.
The convicts were employed carving storage silos out of the sandstone, quarrying the sandstone for building works, including Circular Quay and the construction of the ships dock on the island which took ten years to complete.
In 1842, there were 323 convicts on the island, which at times grew to 500 plus. The settlement closed in 1869, by which time I suspect there were no "convicts" (in the transportation sense) left - I assume it was by then a "regular" prison.
There was only one escape - Frederick Ward in 1863, who was to become the bushranger Thunderbolt.
Much of the old gaol remains, and the tour is worth doing.
To see some images of Cockatoo Island click the following links: