@ Odin
It isn't certain what the ashes are from. Three ideas are:
1) A ball
2) A piece of bail
3) Lord Darnley's Mother-in-law's veil
Whatever those ashes are, they don't ever stay in Australia. In fact the recent tour of Australia by the real ashes in a secure glass cage is very rare. They usually don't leave England.
A replica urn is handed to the winning team. So like Agafaster says, it is the title, not the actual ashes that matters.