The United Nations High Commissioner for Refugees is helping migrants fill out asylum applications. Governors of Mexican states are issuing messages to welcome them. On the U.S. side of the border, some shelters are overflowing already and have started looking for ways to expand the number of available cots.

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More than 1,000 miles ahead of them lies the United States, which the Trump administration insists they will not reach. The Pentagon is expected to dispatch 800 to 1,000 troops to support Border Patrol agents responsible for keeping the migrants from crossing the border.

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Most of migrants have some idea what lies ahead, having heard reports of President’s Trump’s tweets asserting the caravan will not be allowed to cross.

“But they’re not coming because they think it will be easy,” said Margaret Huang, executive director of Amnesty International, speaking on the phone after touring a migrant youth detention center in Texas. “They’re coming because the alternative is unbearable. They’re fearful of what they might end up facing here, but they’re anticipating it has to be better than where they’re coming from.”

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History suggests that most of them may not make it to the U.S. border. After estimating the caravan size at 7,000 on Monday, the Mexican government counted 3,630 migrants in the caravan on Wednesday.

“Conditions are very harsh,” said Maria Rubi, a UNHCR official in southern Mexico with the caravan. “The blazing sun is very demanding. They’ve been walking for a long time, a long distance, with small children and people with disabilities. Some people are starting to ask how they can go back to their countries. The longer the journey goes on, it will happen more and more often.”

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They will not be the last. Behind them, on the Guatemala side of the Mexican border, are more than 2,000 people. Other caravans are en route from Guatemala and El Salvador.

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The UNHCR was expecting to help migrants fill out 23,000 asylum applications this year, even before the latest caravan arrived.

The Mexican government, under pressure from the Trump administration to stop the caravans from reaching the U.S. border, dispatched troops to the Guatemalan border to keep the caravan from crossing. They erected a fence, but thousands of migrants swam or took rafts across the river. Since then, the outgoing government has said it will adopt a more humanitarian attitude toward the migrants, while the incoming government has expressed a distaste for pursuing and detaining Central Americans fleeing misery and violence.

Humanitarian groups started helping them before they departed.

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The International Committee of the Red Cross gives migrants leaflets advising them how to make the journey safer. They tell them what type of walking shoes to wear, suggest taking water-purification pills and to hydrate their children every two hours. They list assistance points where they can stop to get psychological support, make phone calls or send emails home and get help if they are mistreated or in danger.

At least two dozen humanitarian groups, many of them faith-based, send representatives to “accompany” the caravans as they advance an average of 25 miles a day. Their mission is to provide support and witness their treatment, said Camilo Perez Bustillo, director of advocacy for the Hope Border Institute in El Paso.

The situation is more uncertain closer to the U.S. border. The shelters in El Paso are full, Perez said. Facebook appeals have been launched to raise money.

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“There’s an increasing impulse to prepare, on the Mexican side and the U.S. side,” Perez said. “What spaces might be available? Where can we get mattresses? Who’s going to staff it? Who will provide medical attention? There might be 2,000 or 3,000 people coming. We’re beginning to get in preparation mode.”

Ruben Garcia, director of Annunciation House, an El Paso network of shelters with 1,300 beds, said they already are short of spaces to handle the routine number of migrants released every week because there is not enough room in the detention centers. If there are no beds in the temporary shelters, the migrants are released to the streets.

“We are aware of the caravan,” he said. “We’re monitoring it. The mayor’s office called to ask me, ‘What are you doing?’ I’ve been telling them it’s premature to know what might happen.”

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If the caravan splinters, as some reports suggest may already have happened, it is uncertain that any one location will get a wave of migrants.

Father Pat Murphy, director of the Scalabrini Casa del Migrante shelter in Tijuana, recalled that a caravan in 2016 started out 2,000 strong but was just 250 by the time it arrived at the doorstep of the United States.

“We’ve had meetings with the government and all the shelters,” he said. “We have room for 600 people. If 4,000 come, it will be up to the government to be more prepared. Usually the caravans don’t come to the shelters. They stay in the plaza trying to force the United States to open the doors.”

Caravans of migrants have been coming to Tijuana for months with less fanfare.

Tijuana already has 2,000 people seeking asylum. Some have been waiting months to get an appointment with U.S. authorities. Murphy estimates 99 percent will not qualify.