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(CNN) College campuses have become new battlegrounds over immigration as student protests pick up around the US in the wake of last week's presidential election.

At universities across the country, students were walking out Wednesday.

Their aim: Pressuring officials to make their school a "sanctuary campus" that limits cooperation with federal immigration authorities.

The protests came a week after the election of Donald Trump, who's said that deporting millions of undocumented immigrants will be a top priority once he takes office.

In the Wash Sq Park fountain now: "We demand that @nyuniversity ...will be a #sanctuarycampus to all it's students." pic.twitter.com/Tem9q24QCp

"Our President-elect changes his stance on this issue all the time...we can't afford instability." #sanctuarycampus pic.twitter.com/wglOyO8AyN

What's a sanctuary campus?

That depends who you ask. Petitions have been circulating at a number of schools over the past few days. Some ask universities to declare their support for undocumented students publicly. Others ask for more specific measures, such as guarantees that the school won't release information on students' immigration status and that university police forces won't team up with the feds in deportation raids.

"Different campuses are doing different things," said Vera Parra, an organizer with Cosecha Movement . "Actions are not necessarily directed at school administration, but about supporting undocumented students on campuses and their fears about what can happen to them and their families under a Donald Trump administration."

What are protesters saying?

New York University students were among the first to walk out Wednesday.

They packed part of Washington Square Park, calling out demands for the school to become a sanctuary and vowing to fight any government immigration crackdowns.

"We will fight for you, we will put our bodies on the line for you." -an organizer of the #sanctuarycampus walkout to her immigrant peers — Chris Welch (@cwelchCNN) November 16, 2016

An enthusiastic crowd repeated each speaker's words, line by line.

'We have nothing to lose but our chains.' pic.twitter.com/SzCgTtl84C — Isabelle Chapman (@Isa_Chapman) November 16, 2016

"We are unstoppable," the crowd chanted.

But not everyone agreed. A man walking by yelled a response: "You can't stop Trump."

Hannah Fullerton, a junior at the school who helped organized the protest, said she's determined to try.

"We know that President-elect Trump could easily change a lot of policies, and we feel very threatened by that," she said. "This is a moment where it's not about whether you're personally affected anymore. We have a duty to not just do something because it affects us, but because it affects those next to us, our neighbors, our community."

Pia Iribarren, a graduate student who's undocumented, said she and many others could be at risk if Trump rescinds the program that gives relief from deportation to immigrants brought to the United States as children.

"I didn't think we'd actually get to this moment," said Iribarren, who immigrated to the United States from Chile when she was a toddler. "And yet, here we are."

Echoing the message, students from East Los Angeles College held a march Wednesday. The campus is located in the heart of the city's Latino enclave.

Nearly 5,000 of some 30,000 students are undocumented, Marvin Martinez, President of East Los Angeles College, told CNN.

California privacy laws will protect anyone from trying to access the identities of the students to determine who's documented and who isn't, Martinez said.

Who else is participating?

In addition to NYU, organizers say students from about 80 schools around the country are protesting.

A map released by organizers shows dozens of campuses. The map isn't official. People can sign up to place their campus on the map with an online form. But it gives a sense of where we might start to see protests popping up.

An unofficial map shows locations of schools that students want designated as sanctuary campuses.

What do others think?

Word of the protests sparked a swift backlash on Twitter, where some users slammed students for participating.

Many said students shouldn't expect their college campuses to protect them. Some called for funding to be cut to schools that pursued a sanctuary campus policy.

I urge all State Governments to withhold funding to taxpayer funded colleges and universities that declare themselves a #sanctuarycampus — Thomas Cole (@NCSU_Tom) November 16, 2016

We live in a world where it is okay to burn flags and turn colleges into day cares for illegal immigrants...WOW AMERICA WOW #sanctuarycampus — Kalasia Richer (@KalasiaRicher) November 16, 2016

Maybe we should walk out on paying into colleges that encourage liberal extremism! #sanctuarycampus — Carrie Hutchens (@CarrieKHutchens) November 16, 2016

How have universities responded?

But Some school officials have expressed support for students.But according to Inside Higher Ed , some schools have responded with statements suggesting that when it comes to cooperating with federal authorities, their hands are tied.

Wesleyan University President Michael Roth said in a statement that he's weighing the idea.

"In the coming days and weeks I will discuss this option with the appropriate offices and Trustees," he wrote . "I will report back to the campus on what we can do in this regard.

Where does this idea come from?

In recent years, local governments across the country have been in the spotlight for fighting back against federal immigration enforcement by calling themselves sanctuary cities

More than 200 state and local jurisdictions have policies that call for not honoring US Immigration and Customs Enforcement detention requests, the agency's director, Sarah Saldaña, told Congress last year.

There's no legal definition of a sanctuary city, county or state, and what it means varies from place to place.