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Administration officials stress that the children are put in deportation proceedings and said there’s never any guarantee they can stay in the U.S. The officials also said the children won’t be eligible for either the immigration bill that passed the Senate last year or Mr. Obama’s nondeportation policy for children, both of which had cutoff dates for eligibility.

But the children can lodge claims of asylum, and some can also file for a special juvenile visa, which is available to children who cannot be reunited with parents in the U.S.

The Houston Chronicle reported this weekend that the flow has so overwhelmed border officials in Texas that they are shipping “busloads” of immigrants to Arizona, giving them a notice to appear for eventual deportation hearings.

Arizona Gov. Jan Brewer sent a letter to Mr. Obama on Monday demanding to know who devised the policy, which she called “dangerous and unconscionable.” She said Homeland Security officials never gave state officials a heads-up.

“I remind you that the daytime temperatures in Arizona during this time of year are regularly more than 100 degrees. Consequently, this federal operation seems to place expediency over basic humanitarian concerns,” she wrote. “The federal government should not shirk its lawful responsibility to care for and properly process these individuals.”