Each morning, Mexican officials learn from their U.S. counterparts how many asylum seekers will be allowed to cross the border that day. The officials pass that information on to the migrants, who have chosen leaders among them to manage the notebook. Those leaders call the names of the people at the top of the list, and add the names of new arrivals, doling out handwritten numbers on tiny pieces of paper.

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“Come back in a month,” one of them instructed the new arrivals on Tuesday.

“You must keep your number,” said another.

As of Tuesday morning, there were 5,030 people here waiting for asylum. Of those on the list, 2,560 are members of the caravan who arrived mostly in the past week. Most don’t know what they’ll do for the next several months of waiting — where they’ll sleep, what they’ll eat or what will happen once their names are finally called.

“We don’t have control over the process, but it’s the only option we have,” said Osman Alexis Vasquez, 36, from La Ceiba, Honduras.

Experts say there are roughly 8,000 caravan members, mostly in Tijuana, with others scattered around northwestern Mexico. U.S. Customs and Border Protection (CBP) officials typically process between 40 and 80 cases a day from Tijuana, claiming they don’t have the capacity to accept more than 100 per day.

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Throughout his long journey with the caravan, Vasquez had remained committed to asylum, even as other members of the group discussed crossing the border illegally. But until Tuesday morning, after five days in Tijuana, he wasn’t sure how he would even begin the asylum process. He and his brother-in-law had mostly been walking laps around a sports complex turned shelter. Then he heard about the notebook.

“I met a guy who told me that this is how you start the asylum process,” said Vasquez, a taxi driver in his hometown who fled once a local gang started threatening him and his family.

Not long after Vasquez’s name was inscribed, Emma Dinora Lainez, 38, arrived in the plaza with her three children. They, too, had left Honduras in October, but not with the caravan. Now she would probably have to wait for the caravan members to be processed before she could begin her asylum claim. Even as the enormous surge of migrants reached Tijuana with the caravan, the daily flow, from across Central America and Mexico, continued.

The notebook was created earlier this year, as U.S. border officials increasingly restricted people from beginning their asylum claims on the American side of the border. That left migrants waiting in northern Mexico without a way to keep track of who was next in line. Although Mexican immigration officials communicate directly with CBP, the Mexican government didn’t have a system to organize the thousands of asylum seekers here. So the migrants stepped in.

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At other border crossings, including several in Texas, there is no list at all, leaving families to sleep on the Mexican side of the border until U.S. officials agree to meet with them.

On Tuesday in Tijuana, it was Vladimir Muñoz, 21, from San Pedro Sula, Honduras, who was one of a group of about 10 manning the list. He has waited for six weeks for his name to be called.

As he helped those whose numbers were called and who were preparing to line up to ask for asylum, he said the number of names on the list had shot up when the caravan arrived.

“The wait was one month, maybe a couple weeks more, before the caravan, but now it’s gone up to two or so — we haven’t even gotten to them yet,” he said.

At 8:20 a.m. Tuesday, Muñoz and the several other migrants who run the list began calling out numbers and names and countries: a handful from Haiti, Cuba, El Salvador, Guatemala and Honduras, but most from Michoacan and Guerrero, states in Mexico where insecurity has deepened.

Among those whose names were called Tuesday was Lorena Rodriguez, 38, who fled Michoacan with her two sons after her ex-husband, who she said was a member of a criminal organization, began threatening them with death. She wasn’t sure what to expect now that she was about to meet with U.S. officials.

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“I hope they let us stay in a shelter while they review our application,” she said.

After beginning the asylum process, many applicants can spend months or even years waiting for immigration judges to rule on their claims. Single men and women are often detained, while families are typically released together with GPS trackers around their ankles.

Since the caravan arrived, Tijuana’s shelters — including the sports complex that has been converted into one — have overflowed. Last week, the city’s mayor declared the situation a humanitarian crisis and asked the United Nations for help.

Already, those needs have become visible. Lainez said she couldn’t find any space for her family when they arrived this week, so they have been sleeping on a street corner.

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Meanwhile, some members of the caravan already have made it clear that they do not intend to wait the months that might be necessary to begin their asylum claims. Some have acknowledged that they don’t have valid claims and that they have begun looking for smugglers to help them get across the border illegally. Experts say that the longer asylum seekers are asked to wait at official border crossings, the more likely it is that they’ll try to cross the border illegally.

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On Tuesday, the Trump administration said it would appeal a judge’s order preventing it from banning migrants from applying for asylum after crossing the U.S.-Mexico border illegally.

In Tijuana, those who remain committed to the asylum process began planning for the next several months of waiting.

“Hopefully, we can get jobs while we wait,” said Jeni Cantarero, 30, who fled San Pedro Sula with her husband and four children, carrying two police reports that she hoped would strengthen her asylum application.