Now Kurdish territory includes a plump new swath of land. In one southern province alone, Erbil, about 400 villages have been reclaimed, according to Nechirvan Barzani, the regional governor. For Mr. Goran, as for most Kurds, it is sweet victory.

"Now we are back in Mosul," he said, pointing to the dot on the map. "We control Senjar and Mosul Provinces. We want to add the other parts of Kurdistan. We have the same economy, language and future. For the rest of Iraq, it's up to them, but for our part, we will govern ourselves."

After decades of deportations, mass killings and other miseries, Kurds are starting to feel for the first time in recent history that it is safe to return their homes. Even in Halabja, a town devastated by chemical attacks in 1988, residents are beginning to come back.

Kurdish political leaders have governed their own independent enclave in northern Iraq under American protection since 1991. In public, they say they want to be part of Iraq, but most ordinary Kurds do not want that. As American authorities propose remaking Iraqi institutions, Kurds say those very institutions — the army in particular — brought them only misery in the past.

"More than 80 percent of the people are for independence," said Farhad Pirbal, a professor of Kurdish history and literature at Erbil University. "It's etiquette, like a game. The politicians say what the Americans want to hear."

But, he continued, the Kurdish leader Massoud Barzani "in his heart" aspires to be president of "the country of Kurdistan."

Kurds are emerging as the most influential force in the political soup of Baghdad today. They are the only group with their own army, and Kurdish fighters — unlike Shiite Muslim and other Iraqi militias — would be allowed to keep their assault rifles and heavy weapons under an American draft proposal.

They are organized and politically conscious. They have a functioning economy in their independent zone, while the rest of Iraq has foundered. The two main Kurdish leaders, Mr. Barzani and Jalal Talabani, speak fluent English and have had dealings with the United States for decades.

"They're definitely the kingmakers, and the question is whether they might also be the kings," said Peter W. Galbraith, a professor of national security studies at the National War College in Washington.

Kurdish politicians talk of pragmatism. After all, the Kurds do not have their own state, but are spread out in four countries: Iraq, Iran, Syria and Turkey. The Kurdish enclave in Iraq is landlocked and could not survive without doing business with its neighbors and with Baghdad, no matter how good its relations with the United States.

"No Kurd can dissuade himself of the right to self-determination, but history and geography have been cruel to my people, and we know the possibility of a Kurdish state in Iraq is a very distant one," said Barham Salih, governor of the eastern Kurdish enclave. "The tangible thing for us is to work for a federal democracy and be a full-fledged Iraqi citizen."

But Kurds have already made substantial gains since the war. In Kirkuk, a northern city that was the center of Saddam Hussein's "Arabization" campaign to replace Kurdish residents with Arabs and give Baghdad more control over the region's oil fields, the local police force is now overwhelmingly Kurdish.

Kurds won another victory today when American forces here detained five members of an Arab delegation on its way to a city council election. The delegates were suspected of having been members of Mr. Hussein's Baath Party. The American commander in Kirkuk, Maj. Gen. Raymond T. Odierno, met with Mr. Barzani on Friday at his Kurdish base.

Alan Chin for The New York Times

Memories of chemical attacks are fanning Kurdish nationalism. Above, a worker at a memorial in Halabja.

Kurdish political parties said today that they were confident they would win the governorship of the Kirkuk region in elections on Tuesday.

The northern city of Sulaimaniya sent more than 100 doctors to Kirkuk. Kurdish militia guard the gates of the Northern Oil Company, the state-owned oil company there. In addition, Kurdish groups appear to be quietly nursing relations with foreign neighbors independent of Baghdad. A Turkish consulate will open in Sulaimaniya this month, and the local government there is pushing ahead on several oil contracts with foreign companies — more to stake out territory than to reap profits.

The strong new Kurdish presence has chafed on the Arab community in the region, particularly in Kirkuk. Arabs there say Kurdish police officers ignore their problems. They also say Kurds, encouraged by newly energized political parties, are moving into houses that do not belong to them.

American authorities are still unsure how to handle the problem. The new American civilian administrator of Iraq, L. Paul Bremer III, cut short a visit to northern cities last week. An American official who spoke on the condition of anonymity said the Kurdish issue was the main reason for the cancellation.

"The Kurds are the wild card in the Iraqi equation," said Professor Galbraith. "If they were given a choice, almost unanimously they would prefer not to be in Iraq. Over the long term, that's a big problem."

The problem is essentially one of trust. The main political parties, the Patriotic Union of Kurdistan and the Kurdistan Democratic Party, have similar aims, but fought bitterly for territory and influence throughout much of the 1990's. The leaders of the parties, Mr. Talabani and Mr. Barzani, seem to have struck a truce since the end of the American-led war. But trusting Baghdad, even if it is run by Americans, is proving difficult.

Mr. Barzani and Mr. Talabani lodged a formal protest with Mr. Bremer last week, saying the new United Nations resolution to lift sanctions and redistribute funds held from oil sales was unfair to Kurds. In addition, many Kurds think the Americans have been too soft and too slow in untangling the Arabization issue, which the Kurds see as the most important issue now.

"Our previous experience is making us anxious," said Nechirvan Barzani, the regional governor and a nephew of Massoud Barzani. "We feel that we're being kept in the dark about what's happening. People are anxious and unhappy with the way the United States is conducting the process."

Since breaking free from Mr. Hussein in 1991, northern Iraq has been a relative oasis of prosperity. Satellite dishes beam dozens of television channels from every roof. Goods fill shops. All large towns have Internet cafes.

The political parties have grown wealthy, in part on renegade trade across leaky borders with Syria, Iran and Turkey, and have ruled with a strong hand. They held elections only once over the past decade, and are dominated by powerful families, personalities and unilateral decision-making. Critics say the biggest challenge for American forces will be untangling that web.

"The society is like a little mosaic of many patronage networks," said David McDowall, author of "A Modern History of the Kurds." "Kurdish political parties today are not that different from the tribes of the 18th century. You don't get democracy as an end product. You get patrons delivering chunks of delivered votes."

Most Kurds say they are aching to re-enter the larger world after decades of isolation. Because of their uncertain status over the past decade, ordinary Kurds did not have passports. They pin their hopes on the United States to modernize Iraq.

"I have never ridden on a plane or a train," said Rooshad Muhammad, 23, a medical student in Sulaimaniya. "We just want to live like normal people."