With the pace of flight increasing from Syrian President Bashar al-Assad's onslaught on rebel bastions like Homs, the country's neighbours are bracing for a refugee crisis of epic proportions.

Despite freezing rains, snowdrifts and a heavy deployment of Syrian troops near the borders, Turkey, Lebanon and Jordan have registered around 20,000 refugees besides thousands others not registered.

For all their long and bitter experience of such moments of exodus, from Palestinians in the 1940s to the million Iraqis who fled sectarian killing after 2003 - many for Syria - the states of the region are not all extensively prepared, though Turkey and Jordan, to the north and south, are beginning to make plans.

When the Syrian refugees first came into his Lebanese border town, Abdullah Taseer found them rooms in people's homes. Now, he has nowhere left to put them but garages and cowsheds.

'The barns were supposed to be our emergency plan, but with the numbers coming in now we're going to have to start using them already,' said the 30-year-old dentist, who spends his free time organizing volunteers to help Syrians streaming over the snowy mountains on the border and into Lebanon's Bekaa Valley.

It's no paradise, especially not in mid-winter. But for Abu Ammar, a 43-year-old carpenter from the besieged city of Homs, it's better than home: 'We want to save ourselves,' he said. 'Forget our money, our car, our home. All we want is to live.'

Yet Taseer, for the hosts, worries what comes next:

'At this rate I don't think we can continue beyond another month or so,' he says, frowning at a chart of statistics he has drawn up showing 2,500 refugees in the Bekaa, more than half of whom arrived in the past month as violence in Syria spiraled.

In Lebanon, a reluctance to recognize the problem officially is hampering international groups like the United Nations.

A worker for an international aid group in Lebanon, who spoke anonymously, said the country's ability to take in more refugees across its eastern border was limited: 'Now we might be reaching the point where the host capacity is exhausted. If you get 10 or 20,000 in a matter of days, then you have a problem.'

Turkish camps

In Turkey, the official number of Syrian refugees in neat rows of white-tented camps has jumped to 9,700 from 7,200 in the last two months. That is a tiny proportion of Syria's 23 million population and most are from districts close to the frontier.

Ankara, which has given safe haven to rebel army commanders and is now vocal in opposing its former ally Assad, has been building a more permanent container camp to hold some 10,000 people set on 30 hectares (75 acres) of land near the border.

'We are ready to house them for as long as necessary. It depends on the situation in Syria,' said a Turkish official who spoke on condition of anonymity.

He said a new camp that could hold some 10,000 is nearly finished - and it could be expanded should the much-feared prospect of civil war in Syria materialize and bring 'tens of thousands' over the border.

Jordan, which so far hosts more than 3,000 registered refugees, has started construction of a possible camp under supervision from the UNHCR. It is already exploring possible further locations in the event of a mass influx.

Reluctant host

But in Lebanon, local aid workers in Bekaa say the government is ignoring worrying signs that such an influx has already begun. In the Bekaa Valley, along Syria's mountainous western border, weekly arrivals last year were about a dozen.

For the past two weeks, residents have been receiving between 30 and 100 Syrians fleeing their homes.

Further north in Lebanon, the number of registered refugees jumped by over a thousand to 6,375 in January. But activists like the dentist Taseer say there are thousands not registered.

Politically torn and all too familiar with the disruptions of war, Lebanon is trying to maintain neutrality with the large neighbor that dominated it until a few years ago. Many refugees are from Syria's Sunni Muslim majority, fleeing forces led by Assad's fellow Alawites, an offshoot of Shi'ite Islam.

Given Lebanon's tense balance among Sunnis, Shi'ites and a host of other communities, any refugee flow poses a political problem - as did the influx of Sunni Palestinians in past years.

The government in Beirut, dominated by allies of the Shi'ite Hezbollah movement which has long been close to Assad and his ally Iran, has been reluctant to acknowledge a refugee crisis.

Without its official recognition of a crisis and permission to build camps, international aid groups like the United Nations High Commission for Refugees (UNHCR) have concentrated on supporting locals like Taseer who are hosting the refugees.

'When we get 10 or 15 families in a day, we manage. But what happens when we get 100 a day?' he said.

'The Bekaa is close to the capital. Any crisis there could fill the valley with refugees.'

Rising violence is already forcing hundreds out of Homs, the heart of Syria's uprising against 42 years of Assad family rule.

Two weeks ago, Abu Ammar - he did not want his real name used out of concern for relatives still in Syria - fled with his family from the home they had been trapped inside for days.

They left with nothing but the clothes on their backs.

Since then, heavy bombardment in their neighborhood of Baba Amro has killed hundreds more and leveled dozens of buildings in a matter of days. Now his cousins and neighbors are struggling to escape and join him in Lebanon - as little as a 25-km journey from Homs at the nearest point but having to dodge Syrian military patrols on the way.

'We can start again from zero,' he said, holding his three-year-old daughter in the tiny spare room of a mosque where his family of 10 sleeps on woolen blankets.

'In Homs there is no life.'

In recent weeks, armed rebels have begun seizing slices of territory in Syria, crossing a red line of tolerance for Assad's forces who are now responding with heavy force. Central Homs, the suburbs of the capital Damascus and Idlib, near the northern border with Turkey, are now facing heavy ground assaults.

'We couldn't leave the house to get food. We would hear women or children scream and cry, but I couldn't help them,' said Abu Ammar, describing conditions in Baba Amro. 'Even the bodies lying in the street, we were too scared to collect them.'

In the north, cold weather has slowed the flow of refugees into Turkey. A few weeks ago, some 50 to 60 people were crossing the border daily but that has dropped back to 15 to 20, according to Turkish foreign ministry official.

On the Turkish-Syrian border, the Boynoyogun camp houses some 1,750 people in 550 tents set in rows on paving stones and lined by fresh asphalt roads. There are school tents, a mosque, latrines and washing facilities.

Some of the men in the camp find casual day work in nearby fields collecting olives. Others saunter about the camp, smoking as women wash laundry and call after their young children.

But they quickly huddle inside their tents as heavy winter rains soak the camp. Torrential downpours caused a nearby river to flood parts of the camp in recent weeks.

'It's not that bad. At least we have food and we are safe,' says one girl, standing outside a food station. She joins a crowd lined up in the pouring rain to wait their turn.

Conditions are grimmer for refugees in Lebanon's Bekaa Valley like Abu Ammar, who lays out pots to catch the rain dripping in from cracks from the ceiling of his room.

Nearby, his children play, forgetting their fears. 'When we first got here they jumped at every noise, my daughter would scream,' he said.

Slowly, his family is accepting their bare little room as a new home: 'The situation in Syria is not going to end anytime soon, maybe we will end up staying here for five years,' he said, staring at his children.

'But we had no choice. We didn't want to be afraid any more. I want my children to live,' he added.-Reuters