July 14, 2014 8:37 AM EDT

NEW YORK, NY — They’re here, finally, but will they get to stay? That’s the life-changing question hanging over the heads of tens of thousands of young migrants who have crossed the border into the U.S.

Based on a day spent observing an immigration court in New York City, most of them can breathe a little easier: No one appears to be ordered out of the country any time soon…

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