With Mitt Romney now all but assured of winning the Republican nomination, he embarks on one of his critical quests of the campaign: finding a running mate who can help him defeatPresident Barack Obama.

Romney took a huge step toward securing the role of flagbearer when rival Rick Santorum bowed out of the race Tuesday, and the chatter about who gets the nod from the former governor of Massachusetts has risen to a din.

But he quickly sought to dispel the notion that he might rush to find a partner for the ticket -- not after the controversy over Sarah Palin, who was John McCain's surprise running mate in their 2008 loss to Obama.

"No list yet," Romney told Fox on Wednesday. "That's a process which has not begun yet, but will probably begin pretty soon."

And so the "veepstakes" gathers steam, with Romney advisors eyeing potential Number Twos and poring over voting records and personal details in what is one of the most rigorous vetting processes endured by any politician.

Protracted strategizing over a vice presidential pick is standard, as a candidate mulls how his choice might impact the election.

Romney trails Obama badly among Hispanics; does he choose a Latino as vice president to neutralize the incumbent's advantage among those voters, who comprise one of the largest minority blocs in the country?

One of the most talked about VP candidates of the moment is Cuban-American Marco Rubio, the dashing US senator from Florida who'd be equally comfortable campaigning in Spanish or selling Romney's conservative credentials to skeptical core Republicans.

"Marco Rubio would bring an excitement to this ticket that it doesn't have with just Mitt Romney," said Richard Land of the Southern Baptist Convention.

Rubio could help win Florida, a swing state which Land said "could be as decisive this year as Texas was in 1960."

That was the last time a vice presidential candidate helped win a large home state.

But John F Kennedy selected Lyndon Johnson of Texas not just to carry that state, but most of the South, and in the half-century since Kennedy's razor-thin victory just a quarter of VP candidates have come from large states.

If history is a guide, Republicans must win the crucial state of Ohio to take the keys to the White House. That brings to the fore Senator Rob Portman, a veteran Ohio lawmaker who served in two roles in the Bush administration and hence has been vetted extensively.

"Portman is not going to threaten voters in the middle with extreme rhetoric," said long-time political observer Norman Ornstein, resident scholar at American Enterprise Institute, a public-policy think tank.

"He's got an enormous amount of Washington know-how and he'll probably make Romney simply feel more comfortable," Ornstein told AFP.

In other words, boring but safe. But the safe bet may not be the right one.

"One piece of conventional wisdom circulating right now is that Mitt Romney should not pick a boring white guy as his running mate," author Keith Koeneman wrote recently in The Huffington Post.

Romney is on the wrong side of the gender gap, with polls showing Obama leading by double digits among women. New Mexico Governor Susana Martinez, the nation's first Hispanic female governor, could check not one but two key boxes for Romney.

Speculation is rampant in US media, with Indiana Governor Mitch Daniels and Wisconsin Representative Paul Ryan, the powerful House Budget Committee chairman, on several short lists. Former secretary of state Condoleezza Rice is also being mentioned.

But the Romney campaign is staying mum.

"We aren't commenting about the VP process now, nor will we talk about it if we earn the nomination," said Romney spokeswoman Andrea Saul.

That's par for the course, according to experts.

"This is the one moment of suspense that remains," said Ornstein. "And that's why presidential nominees try to keep that news from getting out.... It would be a real change if in fact Romney decided to respond to all this speculation by choosing somebody before August."

McCain waited until late August before stunning the world by choosing Palin, a virtual unknown short on national experience.

The pick energized conservatives, but Palin made several gaffes and the turmoil surrounding her on the campaign was seen as a liability for McCain.

"I don't think Romney will take a big risk like that," said political science professor Alan Abramowitz of Emory University.

"Most likely he'll pick a solid conservative with a track record in the Senate or as a governor."

Even if Romney makes an inspired VP pick, "there's no evidence at all that you get a big boost" from the running mate, Ornstein said.