Kateryna's parents woke her at 5 a.m., told her to pack her documents and phone and flee from their home in Dnipro in eastern Ukraine to relatives in Poland.

It took the 19 year-old three days to reach the Medyka border crossing in Poland, some 1,000 km (620 miles) from Dnipro. It was the first time she had travelled alone, without family or friends.

But waiting to board a train to stay with an aunt living in the western Polish city of Wroclaw just hours after she arrived in the country, Kateryna, who did not give her last name, said she now felt safe.

"Everybody helped me so much," she said.

Aid agencies say that like Kateryna many of the 1.3 million people who have fled Ukraine since Russia's invasion began on Feb. 24 have ties to the large Ukrainian diaspora - family or friends, with whom they can seek shelter.

That has helped relieve pressure on government-sponsored reception or refugee centres that have cropped up alongside Ukraine borders across central Europe in schools, conference centres and tents.

It has also meant the refugee crisis, the fastest moving in Europe since World War Two, has yet to produce the kind of vast migrant camps that cropped up in Greece and elsewhere during a 2015 wave of migration to Europe by mostly Syrians fleeing civil war.

"At the moment we are observing people going where they have connections," United Nations High Commissioner for Refugees (UNHCR) Filippo Grandi told Reuters in a phone interview.

Speaking after visiting Moldova's border with Ukraine, Grandi said that as Russian forces press on with their assault, refugees with fewer resources will flee. "This will be a more complex situation," he said.

Grandi tweeted on Sunday: "More than 1.5 million refugees from Ukraine have crossed into neighbouring countries in 10 days."

Brussels district authorities have set up an online form for those who want to host Ukrainians which includes questions such as whether children or smokers are welcome.

In Germany, refugees are distributed to federal states and from there to individual districts and towns to organise housing.

A total of 227,446 Ukrainians have fled to Romania since Feb. 24, including 31,628 on Saturday, border police data showed. Of the total, 155,680 have already driven or flown out of Romania.

'IN FOUR HOURS, THEY WERE WITH US'

Poland, which has Europe's largest Ukrainian community of 1.5 million, has seen at least 800,000 refugees arrive in just over a week.

But as of Friday, only 20,000 people are staying at reception centres and hotels set up by the government to host over 250,000.

"The rest are with family and acquaintances," said the Polish prime minister's chief of staff, Michal Dworczyk.

Complete strangers help, too, in what has become a massive, very loosely coordinated volunteer effort.

Marek Piasecki, who makes gyroplanes, said one of his sons signed him up on a website placing refugees with families the same day Russia launched its invasion. A day later, he got the call.

"We were told on Friday that two women and two children would be arriving," he told Reuters from his home in a suburb of capital Warsaw.

"Four hours after we got information about them, they were in our home," he said.

But he said he worried that many people were unprepared to care for complete strangers. "In such situations the state really is the best option, because people will want to return to normal life quite quickly, both the hosts and the guests."

The city of Warsaw has set up accommodation centres in public gyms as well as hotels and office buildings, but nearly 4,000 rooms or apartments have also been offered by residents.

At a coordination centre in the Czech capital Prague, Alyona Kubanskih, a 20-year engineering student from the eastern Ukrainian city of Zaporizhzhie, said she was heading to stay with friends of a friend in Prague.

She is one of about 50,000 Ukrainians to reach the Czech Republic, where over a quarter of a million of Ukrainians already live, by Friday.

"I actually never crossed borders before, so it's all new to me. I had never left Ukraine before," she said.