LOS ANGELES — Families hoping to win release for the thousands of migrant children being held by federal immigration authorities are finding they have to navigate an exhausting, intimidating, and sometimes expensive thicket of requirements.

Candidates for sponsorship must produce a plethora of documents to prove they are legitimate relatives and financially capable sponsors, including rent receipts, utility bills, and proof of income. Home visits are increasingly common.

And once those conditions are met, many families must pay hundreds or even thousands of dollars in airfare.

“The government is creating impossible barriers and penalizing poverty,’’ said Neha Desai, director of immigration at the National Center for Youth Law in Oakland, Calif.

An estimated 11,000 children and teenagers apprehended after crossing the border are housed in up to 100 government-contracted facilities across the country.

Their numbers have grown in recent weeks as the Trump administration has imposed a “zero tolerance’’ policy, purporting to end the strategy of “catch and release’’ under which migrants were often allowed to go free pending hearings in the immigration courts.

Under the most controversial part of the new strategy, more than 2,300 children were separated from their families and placed in shelters occupied mainly by young people who had made their way across the border alone.

President Trump relented and ordered that families be kept together whenever possible, but authorities are struggling to process the estimated 2,000 separated children still in federal facilities.

The Office of Refugee Resettlement, which has official custody of migrant children under detention and establishes conditions for releasing them, has made it clear that the requirements are intended to make sure children are not released to traffickers and will be well cared for in their new homes.

In testimony to the Senate in late April, Steven Wagner, acting assistant secretary of health and human services, said that in assessing a sponsor’s suitability, the agency “evaluates the sponsor’s ability to provide for the child’s physical and mental well-being but also the sponsor’s ability to ensure the child’s presence at future immigration proceedings.’’

The requirement for sponsors to pay transportation costs has long been part of the agency’s procedures and was not initiated by the Trump administration, officials said.

Immigrant advocates say that migrant families often have spent their savings to reach the United States and that their relatives here may not have much money, either.

One potential sponsor was rejected recently because authorities decided she could not afford the child’s medication, Desai said. A mother of two was told that her house was not large enough to accommodate a third child. Another was told that she had to move to a better neighborhood.

A new condition requires that all adults in the household where a migrant child will reside submit fingerprints to Immigration and Customs Enforcement. Such a requirement has intimidated many unauthorized immigrants, who represent the majority of sponsors but fear being targeted for deportation themselves.

“Previously, people readily identified themselves’’ to sponsor a child, said Lisa Rivera, managing attorney at the New York Legal Assistance Group. But, she added, “This is not an environment where someone is going to call and say, ‘I want to take my child, niece or nephew.’ They have to find someone who has legal status.’’

Brenda, a Salvadoran migrant who was separated from her 7-year-old son, Kevin, at the border on May 27, was charged $576 to cover the boy’s airfare from Miami to Virginia.

“I was shocked that they had to pay for the boy’s airfare,’’ said Astrid Lockwood, the lawyer for the mother and child.

Lockwood said that in a decade of practicing immigration law she had never seen this requirement but noted that she also had not encountered children placed in facilities thousands of miles from their ultimate destination, as has occurred in recent weeks.

Under the policy manual of the Office of Refugee Resettlement, sponsors are responsible for paying transportation costs for both the child and any escort, along with airline fees for transporting unaccompanied minors.

The payment requirement was also in place during the Obama administration, although it was waived in 2016 when a surge of families crossing the border created large populations in migrant shelters.

Shelter operators were instructed to pay for transportation to enable families to reunite more quickly and were then reimbursed by the government, said Bob Carey, who led the refugee resettlement office during the Obama administration.

The thinking was that it was “counterintuitive to keep a child in care,’’ he said.