In Daquq, a dusty sprawl of 130 villages just south of Iraq’s oil-rich city of Kirkuk, a long-burning cycle of revenge is quietly gearing up for another round.

The battle is a quiet one, fought in the margins of the main war between Iraq and its allies and the militant jihadists of ISIL. It’s not about all-out fighting, but retribution – a settling of scores.

In Daquq, the score being settled is between Kurds loyal to Erbil, the capital of the semi-autonomous Kurdistan Regional Government, and the Arabs many of them believe have no right to live on what they believe is Kurdish land.

Last summer when ISIL swept in from the west, many Iraqi Army forces, which were at that time in control of Kirkuk and the oil flats to the south, abandoned their posts. Kurdish Peshmerga flooded south to keep Kirkuk – and its oil – from ISIL’s clutches. They defended the city of 400,000, but it was close: by autumn the frontline with Isis was a just sniper’s shot west of the highway that cuts from Kirkuk all the way to Baghdad, 150 miles to the south.

As Peshmerga have wrested Daquq’s villages out from under ISIL control, Arab residents say they have not been allowed to return home.

Peshmerga say this is for residents’ own safety from IEDs and sneak attacks by ISIL: “When we consider these areas safe to live, people can come back,” General Sardar Abdul Wahab told The National in his headquarters in the Daquq village of Kheir Wali.

But in the villages under General Abdul Wahab’s control, something about the story doesn’t quite ring true.

The Daquq villages General Abdul Wahab and his men showed this reporter were eerily empty, stripped bare of furniture, vehicles, appliances and the detritus of daily life.

In Wahda, house after house had been parsed even of light bulbs and electrical wiring. Scorch marks inside houses spoke of burning, and the looting appeared to be methodical: there was nothing left. Peshmerga denied they had anything to do with the pillaging, insisting that locals and ISIL, took all household goods.

In other villages, houses hadn’t just been emptied and scorched, but knocked down. Aid workers who serve the area, all speaking anonymously for fear of angering local leaders and losing access, said the destruction wasn’t a result of fighting between Peshmerga and ISIL, but the work of the Peshmerga after ISIL had left.

“The houses are being destroyed after the conflict. Most of these houses are sustained by two pillars at the front. The pillars get knocked over and the house just falls,” one aid worker based in Erbil told me.

“They take the trucks and burn the fields. It’s total destruction designed to force Arab residents out,” he said.

Abu Ahmad is a 40-year-old Arab resident of Wahda displaced to a neighbouring village since Isis attacked in June 2014. He said he and his neighbours had witnessed the destruction of their village by men in the baggy khaki trousers and shirts worn by the Peshmerga.

“After they took everything, they burned the houses with tyres. Every day after, new houses were burning,” he said.

He and his neighbours have yet to return home, despite Wahda being cleared of Isis in March. “We hate Da’esh [ISIL], but we know they didn’t do such a thing. It was the Peshmerga,” he said.

Although Peshmerga on the ground deny any responsibility for destruction or looting, further up the chain of command, the answer changes.

Saed Kakei, a senior adviser to the minister of Peshmerga, confirmed that in some cases, Peshmerga had indeed looted. But what is relevant, he said, is the broader picture: “This matter must not be used against one party while ignoring those who were the main causes of fighting and war.”

This, says Leena Grover, a legal expert on international human rights and a research fellow at the Swiss National Science Foundation, is a critical point. “The description of the justification provided for the pillaging does seem to fit the definition of collective punishment, which is prohibited under international law, including as a war crime,” she said.

But Kakei scoffs at the suggestion that Peshmerga are collectively punishing Arabs, and instead focuses on the historical context of Arabisation.

This is the bigger picture he refers to when he considers what, to many, is the most pressing question in Northern Iraq right now: who is to control the newly accessible areas won back from ISIL? At its most pointed, this is the question of who should control Kirkuk and its valuable oilfields.

Should it be the Kurds, long brutalised by Saddam Hussein’s regime, now on the cusp of declaring their own state and eyeing Kirkuk as the jewel in its crown?

Or should it be Baghdad? For generations, Saddam Hussein forcibly expelled Kurds from the villages of Daquq and replaced them with Arabs who would be loyal to his rule. Arabisation unnaturally altered the ethnic and political make-up of much of Iraq and sowed a hatred and resentment that still festers today. Baghdad today still wants Kirkuk as part of a federated Iraq as much as it ever did – but as sectarian violence continues to blaze throughout the country, hopes for a federated Iraq are fading.

There’s another option: it could be both. Experts say this is the most historically accurate way forward.

“The whole notion that these areas, the disputed territories, were always Kurdish is crazy, just as the whole notion that they were always Arab is crazy. Historically, they are mixed areas,” said Joost Hiltermann, Mena programme director at International Crisis Group, a conflict prevention organisation.

But for two groups locked in a cycle of collective punishment and retributive violence, such an outlook is almost untenable.

Kakei, the adviser to the minister of Peshmerga, insists it’s not a case of blanket hostility towards an entire ethnic group, but rather, reversing the policy of Arabisation.

“The majority of the Kirkuki Kurds do not have negative feelings toward aboriginal Arabs. Rather, their quarrels are with those who were and still are parts of the infamous Arabisation policy, which is still in effect to this very day,” he said.

Kirk Sowell, a political risk analyst based in Jordan and publisher of the biweekly newsletter Inside Iraqi Politics, says Kakei’s view is typical of the official position of the KRG “and any educated, English-speaking Kurd you speak to: that Arabs in these areas should not be physically assaulted, but should be required to leave and compensated for their property”.

“The Kurds’ goal is to undo Saddam Hussein’s Arabisation. The Kurdish goal is not to fight [ISIL]. Saddam is more the enemy than [ISIL] is,” says Sowell.

For Hiltermann, the idea that Arabs should be removed from Kirkuk, among other areas, speaks to a toxic, black-and-white mindset. “The premise is a zero-sum game mentality: they did this to us, and if we don’t do it back to them, they’re going to keep doing it to us. It assumes that people can’t live together.”

“Arabisation was a terrible thing, and led to genocide – I don’t discount that. And people thrown off their land and stripped of property they owned have a right to have that restored to them. But there is such a thing as due-process rights for everyone concerned.”

Part of the problem in Wahda, across Daquq and throughout the stretches of Iraq known as the disputed territories, places both Baghdad and Erbil claim as their own, is a lack of functional mechanisms of transitional justice.

Iraq’s 2004 Interim Constitution established the Iraqi Property Claims Commission, which, due to its own structure and the ongoing conflict, failed to address the situation in any meaningful way.

Two years later, in 2006, the Iraqi Transitional National Assembly replaced the IPCC with the Commission for the Resolution of Real Property Disputes. This body, too, has been unsuccessful in making inroads into long-simmering disputes. Curiously, Arabs forcibly removed from their homes in Northern Iraq by Kurds or others after April 9, 2003 are unable to claim redress with the body.

“Land restitution efforts as an element of transitional justice are always fraught with complexities and challenges. In Iraq, millions of individuals have been displaced in large waves over time for different reasons,” said Grover, the human rights law expert.

“The measures taken by the Iraqi government to date are intended to offer claimants a legal avenue for redressing past injustices and thereby deter the resort to violence. Though far from perfect, reforms have been adopted over the years to improve the performance of the commission tasked with deciding property claims.”

The ongoing conflict and persistent sectarian violence and suspicion are factors in the failure of these measures to deliver results.

The chaos has escalated to a point where, as Hiltermann puts it, “It’s a free for all, grab what you can, take more in case you need to negotiate.”

“Even if it’s rightfully yours, how you regain it is just as important. You can’t violate others’ rights,” he says.

“If people benefited from Arabisation and the previous regime, it doesn’t mean they acquired things illegally. Maybe some of them did, but it needs to be examined on a case-by-case basis.”

In the case of Wahda, many of the Arabs who allege they are being collectively punished by Kurds are in fact the children of the Arabs who arrived with Arabisation. The conflict has been passed down to the next generation.

Abu Ahmad, the Arab resident of Wahda who was born in the village to parents who had moved there as part of Arabisation, said all he and his Arab neighbours wanted was to get along with their Kurdish neighbours.

But for a population bent on re-engineering a past demographic shift, making peace with the descendants is unlikely to appeal, especially when the broader context – the conflict with ISIL and the population movements this has brought about – offers opportunities for boundary changes and power shifts.