Contractor Among Contractors
blacjac has more data than eek
That clears things up then, once the current cotract date is passed, you have no oligations to the client and they have no obligations to you. You can walk away instantly, unless you have indicated you wish to renew.
A 'rolling' contract is a bit more complicated, where there is often an end date on the contract however there wil be a clause that states something like "this contract will automatically renew for another 3 months once the end date is reached, and continue to renew every 3 months, unless either party gives <some time> notice before the end of a 3 month period"