(Repeats story unchanged)
* Charities support displaced in absence of functioning government
* Hundreds of thousands uprooted by conflict
* Turkmens along sectarian lines
By Alexander Dziadosz
BAGHDAD, Aug 15 (Reuters) - School is out, but northern Baghdad's classrooms are packed - not with students, but with people who have travelled further than most to escape the Sunni militant onslaught splitting Iraq.
While perils faced by members of the Yazidi minority fleeing the hardline fighters of the Islamic State have filled television screens for days, the fate of the Turkmens is less well known.
Iraq's third largest ethnic group after Arabs and Kurds, they include both Sunnis and Shi'ites and have a history of being targeted in previous conflicts.
Over the past two months, thousands of them have traveled hundreds of kilometers to the capital to escape the Islamic State insurgents, crowding into schools run by volunteers and religious charities in the absence of government help.
"If you saw their situation when they came, the women and children, the dirt and mud, they were suffering," said Saleem Sahi, a 48-year-old volunteer managing one school where he said children panicked when they saw helicopters flying overhead.
The long journey has separated families that sometimes spanned sectarian lines. Almost all those who ended up in the northern Baghdad schools, near the sprawling Shi'ite district of Sadr City, are themselves Shi'ites.
Other Shi'ite Turkmens have been flown south by the government, which is led by politicians from the country's overall Shi'ite majority, to spare them a perilous journey.
Ibrahim Hussein, 59, a Shi'ite government employee from the northern town of Tel Afar, said that while Islamic State militants might have killed him for his faith, sect had had little impact on local relations before the insurgency.
He pointed to Mohamed Saeb, a 22-year-old Sunni sitting across the room whom he had taken into his home after a suicide bomber killed the young man's family in 2009. "He's become like my son," he said.
NO GOVERNMENT HELP
Volunteers said aid agencies had offered some food and mattresses for the displaced, but those officials who had visited had done so only in a personal capacity, leaving communities and charities to find their own solutions.
A charity affiliated with Iraq's leading Shi'ite cleric, Grand Ayatollah Ali al-Sistani, oversees one school and Sahi said food was provided largely by donors who would have given it to Shi'ite pilgrims in more peaceful years.
One 40-year-old Shi'ite woman from Mosul, northern Iraq's largest city which was overrun by the Islamic State and allied Sunni militias in June, said she was forced to leave her Sunni husband behind when she fled.
Like others, the woman, who asked to be called Umm Abdallah, expressed a cautious hope Iraq's new government might be able to do more to resolve the conflicts scattering them across the country than outgoing prime minister Nuri al-Maliki's had.
Maliki, who after relentless pressure from domestic and international opponents, said on Thursday night he was stepping down, had been accused by critics of worsening the conflict by alienating Sunni Arabs and Kurds.
"We haven't seen anything get better," Umm Abdallah said, looking around the classroom stacked with gas canisters, sacks of flour and cooking oil.
One of the most pressing issues for the displaced is what to do when the school season starts in about a month. Volunteers say they have no idea what will happen. Everyone says the government should act, but no one expects it will.
Sahi said he may try to set up tents in a nearby area. A local official had suggested moving the refugees to a desert area, but Sahi said he was afraid this would isolate them from those providing support.
He was sober about the chance the government would provide any solutions soon, saying it would probably take at least a year before they were able to offer anything.
"We've been going backwards, it's been getting worse," he said as a television blared patriotic songs over images of men dancing in military fatigues.
"The government still needs to be formed," he said. "I think it will take a while."
Sitting in a bare concrete room in one primary school, Hashem Abbas, a 58-year-old Turkmen repairman, said he fled his hometown of Tal Afar in the middle of the night two months ago after shelling by the Islamic State leveled neighbouring homes.
Abbas and his large family made their way first across the mountainous north and eventually to Baghdad, where a contact said they would find shelter. They arrived with little more than the clothes they were wearing.
"Our future isn't clear," Abbas said as a fan rumbled to ease the baking midday heat. "We don't know what will or won't happen. We just ask that God returns us to our homes and our people."
Those assisting them were not sure how that would happen.
"The government has passed away," said Sadeq Sabah, a man volunteering to help oversee one of the schools, pressing his hands together as if in prayer. "There's no one."
(Additional reporting by Maggie Fick; editing by Philippa Fletcher)