BAGHDAD — When Iraqis were drafting their Constitution in 2005, the parties could not agree on who would control Kirkuk, the prized oil capital of the north. They couldn’t even agree on who lived in Kirkuk, which is claimed by the region’s Kurds, but also by its Turkmen minority and Sunni Arabs. For that matter, they couldn’t even agree on where Kirkuk was — in Tamim, Erbil, or Sulaimaniya Province.

So the Iraqis punted, inserting Article 140, a clause that called for a national census, followed by a referendum on the status of Kirkuk, all to be held by the end of 2007. What followed were a succession of delays, against a backdrop of sectarian violence and warnings that Kirkuk could blow apart the Shiite-Kurdish alliance that has governed Iraq since the Americans invaded.

Massoud Barzani, president of the Kurdish regional government, warned two years ago that if “Article 140 is not implemented, then there will be a real civil war.” He’s still waiting.

But so is the threat of civil war, which lurked quietly in the polling places this weekend as residents of Iraq’s Kurdish-dominated areas voted for their regional president and Parliament. Until the status of Kirkuk is clear, nobody really knows how much power those regional officials can wield within the national government, or even whether the Kurds will want to remain part of Iraq.

The problem with settling that is the Kirkuk referendum. There can’t be a referendum until Iraqis figure out who is eligible to vote in Kirkuk, which they can’t do until there’s a census. And any attempt to hold a census in this country may well end up, all by itself, provoking a civil war.

Even now, Sunnis don’t agree that they’re a minority of the nation, and that the Shiites are the majority, though it’s patently obvious. And in Kirkuk, everyone is in denial, one way or another.

Ethnically mixed and awash in oil, Kirkuk has always been something of a numbers game. There are 10 billion barrels of proven oil reserves — 6 percent of the world’s total and 40 percent of Iraq’s — all within commuting distance of downtown Kirkuk. Its fields, though half destroyed, still produce a million barrels of oil a day.

Both Turkmen and Kurds claim to be in the majority; the last reliable estimates, from a 1957 census, gave Turkmen a plurality in the city and Kurds a plurality in the surrounding district, with Arabs second in the countryside and third in the city. In the Saddam Hussein years, the Kurds declared Kirkuk part of their autonomous region of Kurdistan, but the dictator sent the army after the Kurdish guerrillas, known as pesh merga, and held onto the prize. He then set about Arabizing it, forcibly relocating families from the south while evicting Kurds and Turkmen alike.

After 2003, pesh merga troops quickly took control of Kirkuk as the Iraqi Army collapsed. Some local Arabs revolted, nurturing an insurgency that still festers. Others simply remained. Meanwhile, Turkmen appealed to powerful patrons in Turkey that they were undercounted and ignored by everyone, and Turkey came to their aid to make sure the Kurds didn’t get Kirkuk, which supplies much of Turkey’s oil. Only the presence of American troops has kept a lid on things; a brigade is still kept in Kirkuk.

And still there is no census. “The Iraqi government for the last three years, every year they say it will come this year,” says Mahmoud Othman, a Kurdish member of Parliament.

A date for a census is on the calendar — Oct. 24. But it is subject to ratification by Iraq’s cabinet, the Turkmen have announced that they will boycott it and Arabs in Kirkuk may well do the same.

One proposal for getting past this problem would be to hold a census everywhere but in Kirkuk. If that happened Kirkuk could end up, in effect, a disenfranchised province when the next general national elections are held in January.

Another suggestion is to hold a referendum on Kirkuk without a census, but that would invite a dispute about the validity of the results.

And then there’s the Lebanese solution, the one that so far seems likeliest: just do nothing. The last census in that sectarian hodge-podge of a country was in 1932; no one would dare hold one now, since the groups who would almost certainly lose representation — Maronite Catholics, Druze and Sunni Muslims — would simply go back to war rather than get counted out.

Already, the Kurdish regional government has been defying Baghdad and issuing contracts to develop its oil fields, including some in Kirkuk. The Iraqi government showed its displeasure by moving its 12th Division, some 9,500 troops, up to Kirkuk; there they have been provocatively patrolling into pesh merga-held areas and setting off a series of minor incidents recently.

“It’s very worrisome that these incidents continue to happen,” said Joost Hilterman, of the International Crisis Group. “Perhaps they will be contained, but the stakes are huge.”

For the moment, there are still plenty of American troops around to do the containing, but all American combat troops are due to pull out by next summer. That doesn’t leave a lot of time to broker an agreement, especially when no one is likely to really want it.