TRENTON - The duo next door - New York Sen. Hillary Rodham Clinton and former New York Mayor Rudy Giuliani - remain heavily favored by New Jersey voters as they seek their parties' presidential nominations.

Clinton, a Democrat, has widened her lead in New Jersey over Illinois Sen. Barack Obama - now at 51 percent to 17 percent - according to the latest Quinnipiac University poll, released yesterday. Former North Carolina Sen. John Edwards was third with 7 percent.

Giuliani's lead in the Republican race over Arizona Sen. John McCain has shrunk by 10 percentage points but remains substantial, at 38 percent to 12 percent, the poll found. Former Arkansas Gov. Mike Huckabee was third with 8 percent, and former Massachusetts Gov. Mitt Romney was fourth at 7 percent.

"New Jersey voters know the girl and boy next door . . . and apparently are sticking with them," said Clay F. Richards, assistant director of the Quinnipiac University Polling Institute.

"There's no Oprah bump in Obama's numbers, and the Huckabee factor is minor in the Republican race," he said.

If Clinton and Giuliani are their party's nominees, Richards said the general election in Democratic-leaning New Jersey likely would be extremely close.

In an October Quinnipiac poll, Clinton led Obama 46 percent to 20 percent, and Giuliani led McCain 48 percent to 12 percent.

Voters were also asked their views on immigration.

Sixty-five percent said immigration reform should focus on stricter enforcement of laws against illegal immigrants; 27 percent said the focus should be on integrating immigrants into society.

But voters said by a 2-to-1 ratio that illegal immigrants' children should be allowed to go to public schools.

Twenty-five percent of those polled said they would not vote for a presidential candidate with whom they disagreed on immigration policy, regardless of whether they agreed with the candidate on all other issues.

The telephone poll of 1,085 New Jersey voters taken Dec. 5-9 has a sampling-error margin of plus or minus 3 percentage points. The survey included 387 Democrats with a margin of error or plus or minus 5 percentage points, and 320 Republicans with a sampling-error margin of plus or minus 5.5 percentage points.