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They descended silently from the unmarked immigration van that had pulled up outside the iconic Benedictine monastery in Tucson, which has been converted temporarily into a shelter for migrant families released from border detention. Bedraggled parents with bedraggled children, in their arms and by their sides, filed into the sanctuary and occupied several rows of pews. A volunteer named Delle McCormick warmly welcomed them.

The monastery was my first stop in a project to chronicle the journey of migrant families traveling each day, by the thousands, from the southwestern border to destinations across the United States on Greyhound buses.

The families would receive hot meals, clean clothes, toiletries, medical care and access to phones to call their relatives. “By the time you leave here, you’ll be relaxed, refreshed and looking good,” Ms. McCormick, 68, assured them, as other volunteers wove through rows distributing water, oranges and bananas and snipping off bands that had been affixed to the migrants’ wrists by the Border Patrol.