President Donald Trump halted his policy of separating families at the border Wednesday by executive order following massive public outcry. But it may have already cost American taxpayers millions of dollars for a policy most of them oppose, according to media reports.

Behind the immigration policy are a handful of companies and nonprofit groups earning tens of millions to house migrant children separated from their parents. Mr. Trump's new order keeps key elements of his "zero tolerance" policy of prosecuting illegal border crossings along the U.S.-Mexico border.

Health and Human Services' Administration for Children and Families operates 100 shelters across 17 states, with 11,786 children held as part of what's called the Unaccompanied Alien Children (UAC) program, according to a report from Yahoo News citing the agency. From May 5 to June 9, 2,342 children were separated from their parents, according to the Department of Homeland Security.

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The UAC program, set up to provide shelter and services for migrant children that cross the border without a parent, has a fiscal 2018 budget of $1.3 billion. Companies are typically awarded contracts that act as an open purchase order, allowing requests from agencies like HHS to be filled quickly until they reach their full amount.

Just before Mr. Trump signed the order ending the family-separation policy, NBC reported that new "tent cities" built to handle the influx of children cost more than keeping families together.

The U.S. Defense Department is preparing to house as many as 20,000 migrant children at the request of HHS, according to media reports late Thursday citing a memo to lawmakers that was confirmed by a military spokesman. The sites, which were requested to be ready as early as July, would be run by HHS and existing contractors, according to the Washington Post. The plan looks similar to 2014, when the Obama administration housed about 7,000 unaccompanied children on three military bases, the Post said.

Here are some companies cited in media reports and government contract listings.

Southwest Key Programs

A large nonprofit organization with about a dozen facilities in Texas, Southwest Key Programs may get more than $458 million in fiscal 2018, Bloomberg recently reported citing government data.

That's the biggest contract in the system of government agencies, companies and organizations administering the detention centers for children, including those taken from their families at the border, the U.S. Department of Health and Human Services said according to Bloomberg.

Southwest Key's facilities got an influx of new children under the zero tolerance policy, accounting for about 10 percent of the minors in its care, said Lizzie Chen, a spokesperson for the organization, in an email to CBS News. An "influx of unaccompanied minors" also increased demand for space in the facilities, which Chen said are licensed for child care.

Southwest Key's shelters include a former Walmart store in Brownsville, Texas, that has come under scrutiny by Congress and the press. The organization's top executive, Juan Sanchez, was paid $786,000 in 2015, up from about $269,000 in 2010 according to Bloomberg. His compensation nearly doubled to $1.5 million in 2016, Bloomberg said, citing tax records for an Austin charter school he founded.

"Southwest Key Programs does not support separating families at the border and we are pleased that the President has ended this policy," Chen wrote. "We believe keeping families together is better for the children, parents and our communities, and we remain committed to providing compassionate care and reunification."

MVM

Based in Virginia, MVM said its contracts cover transport services for undocumented families and unaccompanied children to HHS facilities. Among the company's contracts is one for to $9.5 million. MVM spent about $3,100 of that total as of this week, according to Yahoo News and GovTribe, which tracks government contracts.

There's a "misperception" about MVM's services, said Joe Arabit, director of the company's homeland security and public safety unit, in an emailed statement. MVM doesn't operate shelters or "any other type of housing for minors," he wrote.

The Daily Beast reported earlier this month that the company posted job openings for "rapid deployment of an emergency influx shelter for unaccompanied children." MVM took down listings "related to readiness operations under the current zero tolerance policy," Arabit said. MVM hasn't "pursued any new contracts associated with undocumented families and children since the implementation of the current policy."

Comprehensive Health Services

Comprehensive Health Services has contracts valued up to $65 million for shelter and related services, according to the Yahoo report and GovTribe. A job listing, one of two dated June 20, seeks a lead case manager to "ensure coordinated case management and family reunification services for children in a children's residential facility." The employee is "responsible for the safe and timely release of all children to appropriate care."

The Florida-based company has received most of available funding through the listed contracts, Yahoo said. A spokesman referred all questions in "unaccompanied alien children" contracts to HHS's Administration for Children and Families' Office of Refugee Resettlement.

Dynamic Service Solutions

Dynamic Service Solutions holds a contract awarded last year valued up to $8.7 million for "shelter care" for unaccompanied children, Yahoo reported. The Maryland-based company's CEO, Darnell Armstrong, referred Yahoo News to HHS for comment. It didn't return a CBS MoneyWatch request to talk about its contracts.

Exodyne

Exodyne was awarded contracts valued at up to $5.6 million through its Dynamic Educational Systems unit, according to reports and GovTribe. The Phoenix-based company didn't respond to a request for comment from CBS MoneyWatch.