WESTBURY, N.Y. — Before dawn breaks and the morning light spills onto his bedroom floor, Carlos Garcia Lobo bounces out of bed, his eyes alight with anticipation, and asks his mother if he can go to school.

Each time, she replies to her 8-year-old son: Not yet.

Four months after fleeing Honduras with a 15-year-old cousin, Carlos has reached what his family said seemed like an impassable frontier. Like dozens of the roughly 2,500 unaccompanied immigrant children who have been released to relatives or other sponsors on Long Island so far this year, Carlos has been unable to register for school.

The impasse has baffled parents, who say their scant resources have proved no match for school district bureaucracies. Required by law to attend school, children are nevertheless stuck at home, despite unrelenting efforts by their parents and others to prove that they are eligible. Suffolk and Nassau Counties, on Long Island, rank third and fifth, respectively, in the United States, after counties centered on Houston and Los Angeles, in the number of unaccompanied minors they have absorbed so far this year; Miami-Dade County is fourth.

Many of the children are barred because their families cannot gather the documents that schools require to prove they are residents of the district or have guardianship — obstacles that contravene legal guidance on enrollment procedures the State Education Department issued in September. Concern over similar deterrents across the country led Attorney General Eric H. Holder Jr. in May to chide districts for “raising barriers for undocumented children,” in that way violating a 1982 Supreme Court decision that guarantees their right to an education.