Tetyana and her two sons, aged 6 and 9, are bundled in black winter jackets and stocking caps inside a small train station in Przemysl, Poland, less than a dozen kilometers from the border with Ukraine.
"I can't hold back tears," she says, recounting the hours since she learned that Russian President Vladimir Putin's troops had launched an invasion of her homeland earlier on February 24.
"My husband is a reservist; he stayed in Lviv," she says.
In addition to President Volodymyr Zelenskiy ordering a general military mobilization late on February 24 and urging able-bodied Ukrainians to volunteer to defend the country from Russian invaders, the Ukrainian State Border Guard Service has barred men between the ages of 18 and 60 from leaving the country.
Tetyana recalled running with her children and her mother-in-law to Lviv's train station to flee, hopefully to safety but unquestionably into uncertainty.
"My heart is broken -- to think of my husband and everything, all the relatives we have left in Ukraine," Tetyana said. "I want to go home as soon as possible. But no one knows what will happen next."
The boys' grandmother, Iryna, said she has no words to describe what has just befallen her country of 44 million people, which Putin has vowed to "demilitarize" and "de-Nazify," in an unfounded characterization that Moscow has used to refer to Ukraine's democratically elected government.
"I couldn't believe the war this morning. That Putin attacked us!" she said. "What mother gave birth to him?"
Iryna also expressed anger that there were so many young men on the train from Lviv to Przemysl: "Here they are.... Who will defend Ukraine?"
It is a scene -- of personal fear and loss, even far from the front lines -- that is unfolding all along the eastern and southern borders of Ukraine, Europe's second-largest and eighth-most populous country.
Polish authorities said that 29,000 people crossed their border from Ukraine on February 24.
Poland has said it can take in up to 1 million people fleeing conflict in Ukraine.
But some governments and humanitarian groups have predicted that a full-scale war will displace millions of Ukrainians, with many likely bound for EU members like Poland, Slovakia, Hungary, or Romania, and others going to non-EU member Moldova.
Within hours of Russia's launch of its large-scale invasion of Ukraine to the north and east, a trickle of families hauled suitcases across the border at the Palanca checkpoint in Moldova on February 24, in search of safety.
It is Moldova's easternmost point, lying low above a bay onto the Black Sea and just 40 kilometers from the Ukrainian port city of Odesa.
None of the travelers were eager to give their names.
Most are from Odesa, the storied "pearl of the Black Sea," with about 1 million residents. But it's also been a provisional headquarters for the Ukrainian Navy since Russia occupied and seized control of Crimea in 2014, shortly before it backed separatists in a war against the government in the eastern Donbas region.
One woman among the heavily laden travelers, with a small child, said she was headed to Moldova to visit a grandfather. Asked whether it was dangerous in Odesa, she said simply, "Not yet."
"There’s martial law and a war going on," said another, a young man. "It’s scary.... There’s shelling. They're targeting military storages and facilities."
Asked why she was leaving Odesa, an elderly woman said as she labored to carry heavy bags: "Because I have to save my family. I'm here with family."
Moldovan lawmakers approved a request on February 24 from Prime Minister Natalia Gavrilita for a 60-day state of emergency to cope with the fallout from the war in Ukraine.
Of the 4,200 or so refugees who arrived from Ukraine on the first day of hostilities, at least 100 were said to have applied for asylum in Moldova.
Many of them hope to continue on to EU destinations.
Pavlo and Svitlana Buklovskiy left Odesa immediately with their 5-year-old son after they were awakened before sunrise by the pounding of missiles slamming the city.
They left behind almost everything they own, taking just a backpack of basic necessities and some of their son's toys.
Within hours they were in the Moldovan capital, Chisinau, where they stocked up before continuing to Romania, hoping to end up in Budapest.
Nearby Romania has also seen an increased number of arrivals, particularly on its northern border with Ukraine.
It shares another 100 or so kilometers of eastern border and 33 kilometers of maritime boundary on the Black Sea -- 650 kilometers in all.
Some families had loaded up vehicles and lined up for gas in the southern Ukrainian city of Chernivtsi before heading the 50 kilometers or so to the border crossing into Romania at Terebliche-Siret.
WATCH: People gathered at the railway station in Kostyantynivka, in eastern Ukraine, hoping to catch a train to safety following Russia's invasion on February 24.
"People are a little worried, because there are three neighboring regions -- Ivano-Frankivsk, Khmelnitsky, and Vinnitsa -- that have already been hit by missiles," Vasile Barbuta, a 28-year-old dual citizen from Chernivtsi, said on February 24.
Around 180,000 Romanian speakers live in the Chernivtsi region, according to official figures.
Most of those crossing into Romania on the first day after the Russian launch of the war were dual citizens, authorities say.
Local officials in Romania, one of the EU's poorest states, say many of the new arrivals want to continue toward fellow members Poland and Czech Republic.
But despite Defense Minister Vasile Dancu's assurance earlier this month that Romania was ready to receive 500,000 refugees in the event of a conflict, Bucharest appeared to be dragging its feet on opening refugee camps.
"We do not want to invite a flow of refugees," a Romanian political source told RFE/RL's Romanian Service, echoing other accounts, after a February 24 meeting of the Romanian Supreme Council of National Defense chaired by President Klaus Iohannis. "If the refugees turn up, we'll ensure the necessary conditions, but we aren't inviting refugees to come to Romania."
Romanian officials were not rushing to make the refugee camps operational, according to multiple sources, and authorities were not actively encouraging those without Romanian passports to fill out refugee documents.
Nicolae Costaș, a professor at Chernivtsi’s state university, said that "everyone is panicking" since Putin launched the invasion, but that Russian missile strikes hadn't yet targeted the city.
He cited "hellish lines" at gas stations and grocery stores and a "big crowd at the border," but he also said local buses were operating normally.
Romania's Border Police insisted the crossing points were fully staffed and equipped, and that they could call in more officers if needed.
But still, long queues were reported at Terebliche-Siret and other Romanian border checkpoints.
NGOs like the Red Cross and the Association of Jesuit Refugee Services, along with UNICEF, said they were closely coordinating with Romanian authorities and ready to help.
Stefan Mandachi, a restaurateur from Suceava, about 40 kilometers from the Ukrainian border, said his businesses would provide a free meal and even accommodation to anyone who identifies themselves as Ukrainian.
"We decided we'll give one hot meal a day to every Ukrainian who comes to our restaurants," Mandachi told RFE/RL's Romanian Service. "If necessary, we'll compartmentalize a large event hall -- it's 1,000 square meters -- so that those who need shelter can sleep."
Other Romanian entrepreneurs have been offering refugees housing and food, too.
And groups have popped up on social media in which ordinary Romanians post announcements aimed at Ukrainians entering the country.
The Uniti For Ucraina (United For Ukraine) group on Facebook has attracted 50,000 members already, including locals and Ukrainian refugees.
French Foreign Minister Jean-Yves Le Drian said on February 25 that EU interior ministers gathering this weekend would look at how bloc members could better cope with the expected refugee problems to come.
"Obviously, Europeans will be there to show solidarity, to welcome refugees," Le Drian told France Inter radio, according to Reuters.