On the subject of who owns what, here are some of the companies listed in your link, Teribus...


1.1. The Corporation shall maintain a registered office in Delaware. (From the by-laws of Anadarko Petroleum Corporation)

Dome Petroleum is owned by Amoco(http://www.geohelp.net/history.html), which is now called BP Amoco (oops! There's at least part of the British raison de guerre with regard to Iraq).

The president and Chief Executive Officer of Vitol is http://www.gts.gov.sg/speaker.htm#sp10Ian Taylor (British, lives in London)

Tigris was founded by Norman Davidson Kelly (Scottish) and its offices are located at 73 Portsmouth Road, Liphook, Hampshire, GU30 7EE according to the UK Patent Office.

BHP Billiton is a joint venture based in Australia (Another member of the "coalition") and the UK.

ENI is located in Texas (US).

Repsol is a Spanish owned company. (Spain was another member of the coalition at the beginning.)

Sonatrach's Registered Office is located in The British Virgin Islands.

And of course, we all know about Shell Oil.

Your link cites AvrAsya Technology Engineering as being Turkish. (Another member of the coalition.)

Your link mentions one company from Malaysia, one company from Indonesia, two companies from Russia, one from India, and one from Canada.

So that's at least four US (one of them a major oil company), and five UK based companies of the ones listed in your link, plus the Turkish and Australian based companies... 11 coalition owned companies that we know of. I don't know whether or not Malaysia, India, or Indonesia were a part of the coalition. Canada was not officially, but it has been providing non-combat support.