WASHINGTON — Call them been-around-the-block Senate hopefuls.

Four of the most contested U.S. Senate races in 2012 feature a former officeholder who hasn’t been on the ballot for a dozen or more years. As majority control of the chamber might come down to a seat or two, the question of whether voters again embrace them — and which ones — may be decisive.

The comeback candidates are former Maine Gov. Angus King, I.; former Sen. and Gov. Bob Kerrey, D-Neb.; former Wisconsin Gov. Tommy Thompson, R; and former North Dakota Attorney General Heidi Heitkamp, D.. Though they can tap the benefits of name recognition, they haven’t been battle-tested in years. Kerrey and Thompson, in particular, have reputations as pragmatic centrists and are re-emerging in a polarized election year.

“The world has changed enormously, and these candidates have to show that they get that,” said Jennifer Duffy, Senate editor of the nonpartisan Cook Political Report.

A quest to return after a hiatus is atypical, though not unheard of, in Senate elections, said Don Ritchie, associate Senate historian. Most recently, Sen. Dan Coats, R-Ind., of Indiana returned in 2011 after a decade away from the chamber spent lobbying and serving as U.S. ambassador to Germany, Ritchie said. Coats was previously in the Senate from 1989 to 1999.

“It gets in the blood politically,” Ritchie said. “People think they’ve left it all behind, but then they hear the siren call again.”

That doesn’t mean it will be easy. Kerrey last ran in 1994 and faces “carpetbagger” criticism in Nebraska after a decade of living in New York City. Thompson, who left the Wisconsin governor’s office in 2001, leads polls in the state’s Republican primary, though he faces attack ads from conservative groups.

In North Dakota, Heitkamp left office in 2001 and is running in a Republican-leaning state. King, an independent who hasn’t been on the ballot since 1998, is the front-runner in polls in Maine and if elected could choose which party leads the Senate if control comes down to one vote.

Republicans currently hold 47 seats in the 100-member Senate and have advantages in trying to gain the majority. Democrats are encumbered by a sluggish economy and hold 23 of the 33 seats on the ballot this year. Also, seven Democratic incumbents are retiring, compared with three Republicans, yielding open seats that pose opportunities for the rival party.

The electoral fate of the veteran candidates will rest on factors including how their past positions play in 2012 and to what degree state politics have shifted. All four states have tilted more Republican and more conservative in recent years.

Kerrey, a former Navy SEAL who served in the Senate from 1989 to 2001, has the toughest battle of the four, said Stu Rothenberg, editor of the nonpartisan Rothenberg Political Report. Kerrey lived in New York City since leaving the Senate, where he was president of the New School, a Greenwich Village institution that touts its progressive and experimental teaching.

After reversing a decision not to run in late February, Kerrey used a friend’s guest house in Omaha as the address for his voter registration, then survived a Republican Party challenge to his residency that went to the Nebraska Supreme Court. The matter is a central criticism of his candidacy.

“Kerrey is a dramatically weaker candidate than he was a decade ago,” Rothenberg said. “Back then he was Bob Kerrey, the guy who didn’t fit into the Democratic stereotype. He was young and dashing. Now he’s the guy who’s lived in New York the last decade that thinks he can just pick up and run back to Nebraska.”

While Kerrey was known for bipartisanship in the Senate, some of his past positions might be a tough sell in a state where President Obama received 42 percent of the vote in 2008. Moderate Democrat Ben Nelson decided to retire from the Senate seat rather than face Nebraska voters again. Kerrey has spoken in favor of Obama’s health-care overhaul and supports a cap-and-trade system to limit greenhouse-gas emissions.

A Public Policy Polling survey conducted March 22-25 found Kerrey trailing state Attorney General Jon Bruning, his most likely Republican opponent, by 17 percentage points.

Kerrey, who declined to be interviewed, is battling TV ads by Bruning, Americans for Prosperity and others contending he’s an opportunistic outsider. He has done little campaigning in the state though has been airing ads that tout his ties to Nebraska and past reputation for bipartisanship.

Former Nebraska Sen. Chuck Hagel, R, said Kerrey has longevity in Nebraska and a knack for retail politics. Still, said Hagel, who won his seat in 1996 after he had lived 20 years outside the state, it won’t be easy for Kerrey.

“He doesn’t have the same liability I had,” Hagel said. “But he’s going to have to work very, very hard to pull this off.”

Thompson, who left the Wisconsin governorship in 2001 and served four years as President George W. Bush’s Health and Human Services secretary, has the broadest statewide name recognition of the candidates in the race for the seat of retiring Sen. Herb Kohl, D.

His election bid is a test of whether Wisconsin voters will support a centrist Republican two years after Scott Walker was elected governor on pledges to slash taxes and spending, said Charles Franklin, a pollster and visiting professor of law and public policy at Marquette University School of Law in Milwaukee.

As governor, Thompson overhauled the welfare system and established a school voucher program, which he promotes to conservatives as accomplishments. Still, some of his past positions — including expanding Medicaid spending as part of a state health-care overhaul and more school funding — are anathema to some conservative groups and Republican voters.

“The party has shifted in the time since he left office,” Franklin said.

Thompson led a field of Republican primary contenders in a March 31-April 1 Public Policy Polling survey, with 38 percent supporting him. Former U.S. Rep. Mark Neumann, his closest opponent, had 25 percent. Neumann is backed by the Club for Growth and a political action committee run by Sen. Jim DeMint, R-S.C., a tea party leader.

Thompson had a narrow lead over U.S. Rep. Tammy Baldwin, the only Democrat running for the seat, in a March 26 Rasmussen survey. He had the support of 48 percent of 500 likely voters surveyed, while she received 44 percent.

In North Dakota, Heitkamp seeks to replace retiring Sen. Kent Conrad, D, in a likely contest against U.S. Rep. Rick Berg, R. As attorney general, she represented North Dakota and 12 other states in a lawsuit against tobacco companies that became part of a 1998 settlement.

Heitkamp has remained active in North Dakota politics in her years out of office. She has worked on three ballot initiatives, including one that required money from the national tobacco settlement to be used for tobacco cessation programs.

Though she has a slight edge over her leading Republican opponent, Rothenberg said, Heitkamp faces risks because Obama won 42 percent of the 2008 vote in North Dakota. Heitkamp said in an interview that she’s confident of her chances.

“North Dakota has always been a state that splits tickets and votes its interests,” she said.

In Maine, former two-term governor King leads in polls in the race to fill the Senate seat of retiring Republican Olympia Snowe. In a March 31-April 2 survey by the Maine People’s Resource Center, 56 percent of 993 registered Maine voters said they would vote for King over the next closest contender, Charles Summers, R, who had 21.8 percent.

King is stressing his independence and highlights an abortion-rights, pro-environment agenda that helped keep Snowe in the Senate for three terms. Republican Gov. Paul LePage’s election in 2010 on the strength of the Tea Party movement doesn’t reflect a lasting shift in voter sentiment to the right, King said in an interview.

He said he’s working to connect with a younger generation of voters and adjusting to a changed world of campaigning that has him hiring a full-time aide just to manage Facebook and Twitter outreach for his election bid.

“I’m going to be asking people to vote for me who never have before, that’s for sure,” he said.