All the oil pumping is done through the Iraqi Oik Ministry, certain contracts have been given out to several multinationals but the majority of the refinares are been or are currently being rebuilt by American and German companies. The profits from the sale of oil are going back into the oil ministry and to the Iraqi people.
Due to current problems with their domestic terror and ethnic tension, refining capacity is still below prewar levels.
Contrary to popular belief, America is not stealing the oil or using it to fund our war. As the former slogan "no war for oil" has proved to be antiwar propoganda. Politics aside, niether politicians nor American oil companies have benefited from Iraqi Oil or the war.