The allure of Kurdish crude continues to tempt western companies, who are under pressure to side with Baghdad in a prolonged political standoff over Kurdish oil rights.
The central government and the Kurdish regional government have clashed over Erbil's insistence to sign production contracts with international oil companies (IOCs). Fearful that autonomy over its energy resources would fan Kurdish separatism, Baghdad has declared them illegal, and refuses to pay companies above the cost of production.
The example of ExxonMobil, which has put its stake in the massive West Qurna-1 field up for sale, shows that the central government is also serious about threats to evict oil majors from oilfields in Iraq's south.
Total, another major that has gone in with Erbil, is hopeful it can avoid Exxon's fate and keep its stake in the Halfaya field in Maysan province, despite an ultimatum from Baghdad to cancel its Kurdish venture.
"It's true that the Iraqi government made the statement that Total will have to choose between assets in Kurdistan and [Halfaya]. But for now we have decided not to choose," said Christophe de Margerie, Total's chief executive, at the Adipec industry conference this month in Abu Dhabi.
If the French company can stall on a decision for long enough, it may keep both assets after Erbil and Baghdad have agreed on an oil law that would legalise its stake in Kurdistan.
"The two parts of this country are in the same country, so we hope that they will quickly find solutions for how they will work together and get together an oil law," said Mr de Margerie.
After years of disagreement, both sides have intensified their efforts to pass the oil law. For the Kurds, the law is crucial, as without it, production in the autonomous region will not become profitable. The central government needs to introduce a comprehensive legal framework for the smooth running of its oil sector.
IOCs are, for the time being, still tempted by Kurdistan.
"There are a lot of opportunities if you want to go for it," said Anders Hatteland, the senior representative for Norway's Statoil in the Middle East.
"One of the things that I find that's interesting with Iraqi Kurdistan is that it's one of these places where you actually have a liquid [mergers and acquisitions] market," he said. "You don't find that in many places [like that]."
After selling its stake in a southern oilfield, Statoil was evaluating its options in Kurdistan, said Mr Hatteland.
One oil major that does not claim an interest in Kurdistan is BP, whose former chief executive Tony Hayward is active in the region with his new company Genel Energy.
"We absolutely remain committed to Iraq," said Bob Dudley, BP's chief executive, at Adipec. The British producer is ramping up production at the Rumaila supermajor field in the south and does not want to risk future business by venturing north.
"We're meeting the leadership of the country about it and exploring other areas of cooperation, but its too early to talk about anything specific," said Mr Dudley.