Some of the migrants in the largest caravan heading north in Mexico have gone ahead of the main group in the state of Veracruz, like these hitching a ride Saturday on a tractor-trailer heading for Cordoba. (Raúl Vera)

They fall asleep on borrowed blankets, curled up on a floor someone has loaned for the night. They share meals of chicken soup and tortillas. They wash laundry in rivers or sinks, and when they fall sick after more than 20 days on the road, the people in the migrant caravan turn to the nuns trailing them with medicines and bandages.

With 4,000 to 5,000 people, the first and largest group trudging slowly to the U.S. border is bigger than some of the municipalities it has descended on in Mexico, doubling their population overnight. They are fleeting guests, a gathering bound by a single goal: seeking asylum or work in the United States.

“It’s practically a walking town,” said Edgar Corzo Sosa, a national human rights official in Mexico monitoring the caravan. As he spoke this weekend, the group was traveling through the southern state of Veracruz, several hundred miles southeast of Mexico City.

Like any town, the caravan has had its share of milestones and tragedies. Babies have been born, one man died after falling from a crowded truck, and several women have had miscarriages, according to Mexico’s Red Cross and rights officials. The migrants rise together at dawn, travel in clumps of families or friends from the same hometowns and hold nightly assemblies to decide where to go next.

It can be a fragile alliance, frayed by exhaustion and uncertainty — and they had hoped it would have ended by now, with buses ferrying them to Mexico City and then north to the U.S. border. But the buses never came.

By Sunday, the caravan had split into groups, as faster-moving travelers hitched rides and jumped ahead on the route. At sunrise, more than 1,500 left the small city of Isla and headed toward Cordoba, also in Veracruz but closer to the capital, while others had scattered into the neighboring state of Puebla and other cities along the way.

Most of the migrants are from crime-ridden Honduras, where the caravan hastily assembled in mid-October as people jumped at the chance to travel safely through Mexico without having to pay smugglers thousands of dollars. Since then, some have turned back. Others have sought asylum in Mexico.

Still others have walked until their shoes fell off along the long, hot road.

Their movements are coordinated by megaphone-wielding members of the U.S.-Mexican activist collective Pueblo Sin Fronteras, although organizers say the caravan governs itself. But the crowds also depend on Mexican cities and towns that offer up community centers where they can sleep and church groups willing to slap together tamales and barbecue in the middle of the night.

President Trump has portrayed the caravan — and others forming behind it — as “very bad thugs and gang members,” noting that on Oct. 19, thousands of migrants had pushed and kicked their way through a border gate from Guatemala to Mexico. His claims were inflamed on the Internet by misleading images, including one of a bloodied Mexican police officer that was taken elsewhere in 2012.

Trump has ordered thousands of troops to the southern border and has said he would consider sending as many as 15,000 — roughly the size of the U.S. military’s presence in Afghanistan.

In Mexico, police and government human rights observers say they have seen no examples of terrorists or extreme violence.

“He can say a thousand things,” Corzo Sosa said of Trump’s claims about bad actors. “We’re here in the caravan. . . . We haven’t identified any.”

On Friday, shortly after they crossed into the state of Veracruz, home to stunning beaches but also deadly cartel-fueled violence, rain-soaked migrants cheered when Gov. Miguel Angel Yunes said he would provide buses to take them to Mexico City.

But Yunes quickly changed his mind, citing a water shortage in the capital. Critics claimed he was pressured to stand down to avoid a clash at the U.S. border before the U.S. elections on Tuesday.

Dejected, the migrants headed north the next day on blistered feet, taking a narrow ribbon of road one organizer said is a frequent site of robberies and attacks, calling it the “route of death.”

Pueblo Sin Fronteras urged them to stick together. But some rushed to hitch rides on tractor-trailer trucks, cramming into the open doors or clinging to the sides.

Oscar Lopez, 31, hung back with his wife and three children, including 3-year-old Elias, who sat in a stroller wearing blue Crocs adorned with racecars.

“That’s dangerous,” Lopez, 31, said shaking his head as others hoisted themselves into the truck. In the tumult of the caravan, his 12-year-old son went missing for 33 hours, he said, and he wasn’t willing to risk it again.

As they waited for safer rides, the food brigade swooped in from Our Lady of the Rosary Church.

The night before, the church’s young priest, Joel Campechano, had alerted his parish over WhatsApp that the caravan was coming. The next day, parishioners served homemade tamales, pots of rice and tortillas.

One of the volunteers was Marta Murgia, 43, who wore a hot-pink apron with a picture of Jesus. “I wonder what’s waiting for them,” she said of the families passing by.

Down the road went the Avaloses, the Lopezes and the Contrerases, including a feverish baby named Aaron, whose mother, Nataly, lowered his temperature with medicine and water-bottle baths by the roadside. Entire hometowns were grouped together, like the contingent from Siguatepeque, a mountain-ringed town in Honduras.

Without buses, it became clear that the journey would take much longer than they had hoped, and some mulled taking a different route. One young man said he was messaging a smuggler friend who told him it would cost $7,500 to cross the U.S. border.

Some jumped in taxis. But many stayed, saying it was cheaper to travel together.

After the 44-mile trip from Sayula to Isla, brothers Arnulfo and Arnoldo Gomez stopped at a gas station to take stock. They had no money. Their cellphones were dead. Arnoldo, at 30 six years older than his brother, wore plastic sandals because his boot soles had fallen off.

Arnoldo Gomez, who left a wife and two children in Tocoa, Honduras, said several women had offered to take him in. He refused to leave his brother and the friends he had made on the road.

“These are the temptations,” he said.

“We have to stay together,” said Jose Guillen, 22, standing near his new friend Alejandro Carvajal, an 18-year-old singer. They were traveling with a group from San Pedro Sula.

At a stop between Isla and Cordoba, Orlando Rodas Martinez, a 22-year-old organizer with Pueblo Sin Fronteras, advised people against splitting up and hitching rides.

“Compañeros, we can’t skip ahead like this,” he told a group. “If there are few of you, it’s easier for the authorities to come and round you all up.”

“Some say one thing, and others say something else,” one man said, and took off.

By Saturday night, the remaining migrants packed Isla’s cavernous social center and spilled onto the streets outside.

Inside the social center, usually reserved for weddings and dances, the caravan rearranged itself as a small village. Families and migrants slept blanket-to-blanket, on blowup mattresses and wooden pallets. Others pitched tents. Laundry was strung from poles.

Maynor Chavez, a 44-year-old father from Copan, set up shop on a yellow tarp, selling shampoo, lollipops and cigarettes he had bought with money donated along the way.

On Venustiano Carranza Street, residents with houses still decorated for the Day of the Dead let migrants sleep on their patios or take showers. The air filled with the sounds of barking dogs and crying children.

Hours later, they were gone.