Pamela Ortiz Cerda vividly remembered the assignment six years ago from her Mexican-American history instructor at San Joaquin Delta College, a community college in Stockton, California. "He required voting for our class," Ortiz Cerda said. Students were told to bring in voting ballot stubs as proof.

"I assumed it was a joke, but to the whole class he said, 'And for you, all you illegals, I'm going to have immigration waiting outside the class for you if you don't have the stubs'," she said. "As a teenager, straight out of high school, that's terrifying."

Terrifying because Ortiz Cerda was unauthorised herself, brought to the US from Mexico when she was nine by her parents, who sought a better life for the family.

Ortiz Cerda, now 24, is the programme services coordinator at Skyline College's Dream Center in San Bruno, California. It is one of about 40 such centres in California that assist students without legal status, navigating the complexities of admissions and connecting them with financial aid. The centres are part of an endeavour to help unauthorised students attain degrees. And while many of these programmes have existed for years, there are concerns about pushback as the Trump administration has shifted to a "zero tolerance" policy on illegal immigration. This has led colleges to develop policies, with California in the forefront, that would thwart possible interference by the federal government.

The concerns are especially acute at community colleges, which have more open admissions policies than selective four-year institutions.

"It is our desire to be there for the most vulnerable and marginalised populations," said Judy C. Miner, chancellor of the Foothill-De Anza Community College District, which serves Silicon Valley.

The official policy of US Immigration and Customs Enforcement is to steer clear of college campuses, unless there is an extraordinary safety threat. But after Donald Trump was elected president, following a campaign filled with rhetoric against unauthorised people, colleges became concerned.

"We don't feel a level of confidence and security on behalf of our students," said Miner, who is past chairman of the American Council on Education, which represents 1,800 higher education institutions in the US. She and her colleagues had taken precautions, she said. At her colleges and others, for example, any warrant from immigration officials must go directly to the college president for review and could be subject to a legal fight.

All of this is a sea change from just a few years ago, when many unauthorised students were given temporary immunity from deportation after the Obama administration's creation of the Deferred Action for Childhood Arrivals programme (DACA) in June 2012. About 8,00,000 immigrants, who were brought to the US as children, were allowed to remain as residents, attend school and obtain work permits.

The Trump administration effectively ended the programme this year, and participants have been left in limbo as Congress considers an alternative, if any, and as challenges work their way through the courts.

Even before DACA, California had its own DREAM Act (development, relief and education for alien minors) in 2011, allowing those brought into the state without documentation as children to attend college and receive financial aid and in-state tuition benefits.

But in the current political climate, unauthorised students in other states have faced resistance. In April, the Arizona Supreme Court eliminated in-state tuition benefits for them, and similar programmes face legal hurdles in several other states.

"There's so much enmity that it's looking very hopeless, honestly," said a mathematics student at Skyline College, who spoke on condition of anonymity. His mother brought him to the US from Mexico at age 13, when she was fleeing a violent husband. He worked at auto shops, warehouses and in manufacturing to support his mother and six siblings. Now, at 41, he has been able to get an associate degree and has ambitions for a bachelor's.

He said he had often faced hostility as an unauthorised person, but not at college. "I don't feel my studying is threatened, at least not yet."

For Miner too, the stakes are personal. Her mother was unauthorised, brought to the US from Mexico at age 3 - in another era, she also would have been a "Dreamer".