Latinos living without immigration papers in Arizona have begun bombarbing helplines and lawyers' offices with anxious requests about how to provide for their children should they be arrested under a controversial new police power that came into effect this week.

A phone line hosted by the Arizona branch of the American Civil Liberties Union has received almost 4,000 calls in just two days, many from anxious parents who fear that their children could be left abandoned should they be picked up under the so-called 'show-me-your-papers' provision. Hundreds have been asking for help setting up a "power of attorney", which gives a relative or friend who has US citizenship the right to care for minors in such an eventuality.

"People are terrified. They fear that they will go to the store to buy groceries and won't get home and their kids will be left alone at school," said Luz Santiago, a pastor in Mesa. She said she has personally handled about 50 requests for power of attorney since Tuesday.

The show-me-your-papers clause is the most deeply contested of the provisions of SB 1070, an Arizona law that was passed in 2010 that has set the benchmark for a wave of hardline immigration laws clamping down on undocumented families that have swept across several states. Under its terms, police officers are required to investigate the immigration status of anyone they come across during normal police work and whom they suspect of being unauthorised.

The law was snarled up in legal challenges that went up to the US supreme court. In June, the court struck down several elements of the legislation but allowed 'show me your papers' to go ahead pending local Arizona court approval.

That approval was granted this week and the provision is now in effect.

Phoenix, the capital of Arizona, is already braced for the new power having witnessed the impact of heavy-handed policing for years under the direction of the Joe Arpaio, America's toughest sheriff. Groups working with undocumented Hispanics are more concerned about other smaller towns such as Flagstaff and Prescott, which have large Latino populations but no experience of police officers acting as immigration agents.

Tucson, Arizona's second-largest city, is calling a forum next Tuesday in which community leaders will meet the police chief Roberto Villasenor to discuss implementation of the clause. Regina Romero, who sits on the city council and who has convened the meeting, said the clear fear was that police would be drawn into racial profiling.

"We live 45 minutes from the Mexican border, so who else other than Mexicans are you going to be picking up? You are not going to be looking for Canadians in this part of the country," she said.

Alessandra Soler, head of the ACLU in Arizona, said that there was already evidence that Tucson police were making contact inappropriately with US border patrol officers even for such mundane issues as help with translation. "It's extremely problematic when you have local police contacting border patrol when there is no good reason."

The ACLU and other groups have an outstanding civil rights action against SB 1070 still lodged with the state's appeal court. That legal attempt to put a stop to 'show me your papers' will continue to pass through the courts, and the intention of opponents of the provision is to beef it up with real examples of racial profiling that might now occur under it.

Lydia Guzman, the director of the hotline, said the aim now was to chronicle the impact of the new law. "The supreme court has given us the green light to present to the courts victims of racial profiling, so that's our challenge: show me the victims."