NEW YORK — More than 81,000 New York City kids started kindergarten in the fall of 2012. By the time they got to fifth grade, one in eight had been homeless, many forced to stay with family or friends or in a shelter.

That’s according to a New York University study released Wednesday that says the city’s student homelessness problem is most rampant among the city’s youngest kids.

The Research Alliance for New York City Schools at NYU’s Steinhardt School tracked the 81,669 students who entered kindergarten in the fall of 2012 for five years. Of the 10,312 students — or more than 12 percent — who experienced homelessness before their fifth-grade year, more than a quarter were homeless for all five years and nearly 70 percent were homeless for more than a year, the study found.

More than half the homeless students “doubled up,” meaning they lived with family or someone else, while another 30 percent stayed in shelters and close to 10 percent “experienced multiple forms of homelessness,” the report says.

The study also revealed stark racial disparities in student homelessness. Nearly 89 percent of the tracked homeless students were black or Latino, the report says — as were almost 95 percent of those who lived in shelters for at least three years.

The latter finding “underscores the disproportionate impact of extreme poverty on NYC’s Black and Latino students,” Kathryn Hill, the report’s other author, said in a statement.

That group of kids is “perhaps the neediest” and also suffered the most stark academic consequences of homelessness, according to the study. Fewer than 20 percent got proficient scores on the state English and math tests, and more than 80 percent were chronically absent, which means they missed roughly a month of school, researchers found.

The kids who experienced homelessness also were not evenly distributed throughout the city, the study found. The western Bronx, upper Manhattan and northern Brooklyn were home to the schools with the highest proportions of them, the report says. And more than 10 percent started kindergarten in The Bronx’s District 10 alone, researchers found.

The proportion of young kids experiencing homelessness outpaces the rate for the city’s entire school system. Some 114,659 students — more than one in 10 — were identified as homeless in the 2017-18 school year, according to data published in October.

The city has ramped up spending on services for homeless students in recent years, and the Department of Education has worked with the Department of Homeless Services to place families in shelters closer to their youngest child’s school.

Schools also often work with community-based organizations that help support students’ needs, according to the NYU study. But those partnerships take a variety of forms, and there’s a need for better evidence about how they help homeless students, the report says.

“Given that so many NYC students experience homelessness during these years, and that schools often engage in partnerships in an attempt to meet these students’ needs, it is important to learn more about what makes these collaborations effective,” Research Alliance deputy director Adriana Villavicencio said in a statement.