Behind that dream, however, Iraqi Kurds and their leaders differ on key issues related to statehood, their future within a unified Iraq, and ties with Kurdish populations in neighbouring countries, all of which are likely to confront the regional parliament as it embarks on a new term.
In particular, voters and the ruling elite appear to disagree on the main upcoming issue: as the three-province autonomous region becomes increasingly economically free of the central government, whether full-fledged independence is in the offing.
"The Kurdish dream of independence is always there, we have a fundamental right to that, but we are hoping that Iraq will succeed as a democratic nation," said Barham Saleh, a former Kurdish regional prime minister who also spent time as the deputy premier in Iraq's federal government.
"The issue of identity is very important, it is a very emotional issue," he continued.
"I am proud of my Kurdish heritage and identity. I very much would like to see an Iraqi state that is democratic -- genuinely democratic -- respectful of individual liberties, that makes us all proud to be Iraqis.
"This Iraq is yet to be realised."
On the streets of regional capital Arbil, however, views towards Baghdad are often much stronger.
"My relationship is with Kurds, all Kurds, wherever they are," said Mohsen Ali, a 57-year-old former fighter with Saleh's own party of ex-rebels, the Patriotic Union of Kurdistan.
Clad in traditional Kurdish garb and sat at a cafe in one of the city's oldest districts, Ali added: "I want to cut ties with the centre. I want to be free, on our own, not connected to anywhere else."
"We, the Kurds of Syria, the Kurds of Turkey, the Kurds of Iran, the Kurds of Iraq, want ... to be free -- one free country."
Kurds make up significant minority groups in Iraq, Turkey, Syria and Iran but have historically faced hostility from those countries' governments.
In Iraq, in particular, Kurdish rebels battled the Baghdad government for decades and suffered from often-brutal repression, notably during the Anfal campaign and the Halabja chemical attack, which remains the deadliest gassing of civilians ever.
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Since 1991, however, they have largely run their own affairs, and now operate an autonomous region that passes its own laws, has its own security forces, and runs its own visa and foreign investment regimes.
As a result, younger Kurds often have little to do with their Arab countrymen -- fewer speak Arabic than older generations, and have the option of exclusively Kurdish satellite television channels and news outlets.
And while much of the Arab-dominated parts of Iraq suffer from regular, and indeed worsening, violence, residents of Kurdistan enjoy relative safety and stability.
"We were second-class citizens," said Mohammed Saleh, an architect who studied at the University of Baghdad until 1979 but, like many of fellow Kurds, expressed a desire for independence.
"The people here do not like to be Iraqi, or feel like real members of the country."
He added: "We have a federal government, but there is no relationship between us and them."
But many are not optimistic for independence, noting that an Iraqi Kurdish declaration of statehood would raise alarm in the region, worsening what have largely been improving ties between Arbil and neighbouring states.
"Everyone -- everyone -- in his heart, or her heart, feels that an independent Kurdistan is our right," said Asos Hardi, a journalist and analyst based in Sulaimaniyah, the region's second-biggest city.
"But ... I think that it would be very hard to imagine that, for example, in the next 10 years we would have an independent Kurdistan.
"I hope that we could build a democratic system in this area and be supportive of other parts of Kurdistan -- to the peace process in Turkey, between Kurds and the Turkish state, and support as much as possible the Kurds in Syria and Iran."
And while many Kurds have expressed strong fraternal links between neighbouring Kurdish populations, one politician pointed to failed moves towards pan-Arab statehood in the 20th century as a guide for Kurds with ambitions for one state.
Laughing while referring to the 22-member Arab League, Abubakr Ali, a senior member of the Kurdistan Islamic Union, said: "Even if there will be independence, there will be four countries.
"And then we will have a league!"