The US is in over all command, but the day to day admin is done by the Brits in and around Basra, this is why we were sent down to that end of Iraq on our own, it makes life easier for Tony Blair, as it's one less accusation that his opponents can throw at him. ie Ceding sovereignty to the US, which is as much of a problem with us Brits as it would be for you guys to let us take command.
Giok