THE governments of countries abutting Syria have long worried that the civil war there may spill over the border, stirring strife across the region. Whereas refugees were leaving Syria last year in a steady trickle, now they have become a flood. In the past few weeks as many as 5,000 people a day have been coming over. Entire villages are emptying out. The office of the UN’s High Commissioner for Refugees (UNHCR) previously said it reckoned 1m people would have fled Syria by June. But already more than 700,000 have done so—and that includes only those who have been registered. The UNHCR will have to reassess an already dire situation.

Agencies and host countries are struggling to cope. Most of the refugees are women and children. In Lebanon there are no official camps, so they lodge with families. Conditions in camps in Jordan and Iraq are grim. Earlier this year rainstorms and even snowy blizzards turned some camps into quagmires. Children died of cold. Some tents went up in flames as refugees stoked fires inside them to be warm. The plight of an estimated 2m Syrians displaced inside the country is even worse, since many are in areas deemed too dangerous for humanitarian agencies to venture. The UN says it is helping over a fifth of the country’s 23m citizens, inside and out. “We are all asking where it will end,” says Panos Moumtzis, who heads UNHCR’s mission to Syria. “This is the most complex and dangerous situation I’ve seen.” For Iraq, Jordan, Lebanon and Turkey, which host nearly all the refugees, the cost is growing. Schools and hospitals are crowded. Neighbouring governments are still more worried by the political instability that a refugee influx invariably brings. The Lebanese are bitterly divided over Syria. President Bashar Assad is backed by the Shia party-cum-militia, Hizbullah, but is hated by Lebanon’s Sunnis. Many Lebanese are afraid that the refugees may upset the country’s fragile sectarian balance.

Jordanians worry that Syrian and other jihadists will use their country as a base, stirring up Jordan’s own Islamists. Turkey is wary of fleeing Syrian Kurds, since it has long battled against its own large Kurdish minority. And Iraq’s Shia-dominated government fears that restless Iraqi Sunnis may be bolstered by their co-religionists fleeing from Syria, who make up the bulk of the fighting opposition to Mr Assad.

Matters have been made worse by the aid agencies’ lumbering reaction. Refugees have rioted over conditions at Zaatari, a camp in the Jordanian desert not far from the border. Médecins Sans Frontières, a French charity which is one of the few to work in rebel-held areas, where it runs field clinics, has complained that too little aid is getting through. This is because the UN works through the Syrian government and its authorised agencies, which tend to favour government-controlled areas. Governments including those in Europe and the Gulf have been slow to fulfil past pledges. The UNHCR says it has received only 3% of the $1.5 billion it has asked for to fund its work from now until June, though at a meeting in Kuwait on January 30th donors promised $1.5 billion, with the emir pledging $300m.

The rich world’s failure to embrace the refugees more generously mirrors the ineffectiveness of its diplomacy. “No one is willing to lead policy on Syria,” bemoans Salman Shaikh, who runs a centre in Qatar for the Brookings Institution, a think-tank in Washington. “Other organisations can work in the north [of Syria], if the UN can’t. The opposition coalition has a plan for humanitarian aid but no one is giving them the money that was promised,” he says.

Western governments are still loth to arm the rebels. Meanwhile, a sea of tents is growing on the Syrian side of the border with Turkey, where refugee camps are already bursting. And Jordan is turning back Palestinians fleeing from Syria, fearing lest they brew trouble among Jordan’s own disgruntled Palestinian people. The Jordanian government has threatened to shut the borders completely if the rate of incoming refugees gets even bigger.

On January 29th around 80 male corpses, their hands bound and heads holed with gunshot wounds, were pulled out of a river near Aleppo. Mr Assad is pummelling rebel-held areas such as the Damascus suburb of Daraya into rubble in his determination to keep them under his control. In such circumstances, the incentive to leave is plainly growing. Syria’s refugee crisis is out of hand.