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Republicans are running out of ways to reclaim their grip on a GOP that many party leaders regard as spinning out of control, now that Donald Trump is its presumptive presidential nominee.

Some have thrown in the towel and reversed course to endorse Trump, having previously condemned him. Some still hold out hope that a third party Republican might at least carry the banner for traditional conservative values. Some plan to sit out both the party's convention on Cleveland in July and possibly the entire election.

But there is one way that anti-Trump Republicans may still yet wield substantial influence over the shape of their party's presidential ticket: the billionaire businessman's choice of a running mate. The Republican Party's rules for nominating a vice presidential contender differ sharply from those that govern the top of the ticket, and give convention delegates considerable control over who ends up as Trump's running mate.

Now that every one of Trump's GOP rivals has dropped out, there's no more talk of a brokered convention or of anti-Trump delegates siding with Texas Republican Ted Cruz, for example, in the second round of convention balloting. Trump is expected to have won the 1,237 delegates necessary to clinch the nomination by the time he gets to Cleveland. Most of those delegates will be bound by state rules to vote for Trump on the first round of balloting.

But GOP delegates "are effectively free agents" when it comes to other decisions that will be made at the convention, including the contents of the Republican Party platform and, crucially, the selection of a vice presidential nominee, says Trevor Potter, former chairman of the Federal Election Commission and who was general counsel to Arizona Senator John McCain when he was the party's 2008 presidential nominee.

"The most important decision they will make is to vote for a vice presidential candidate," notes Potter, who knows full well how contentious such choices can be. When McCain arrived at the GOP's convention in Minneapolis-St. Paul, Minnesota, in 2008, he was seriously considering tapping as his running mate then-Senator Joe Lieberman, an independent and former Democrat who had run alongside Al Gore in 2000.

But McCain's advisers warned him that selecting Lieberman, an abortion rights supporter, would trigger an all-out conservative revolt. McCain "decided not to risk a floor fight," recalls Potter, though he argues that the Arizona Senator would have won that battle. McCain ultimately chose then-Alaska Governor Sarah Palin, a conservative firebrand who soon thereafter proved highly controversial. In this election Palin has endorsed Trump but says she would not consider another tour as running mate.

Trump could be headed for a nasty floor fight himself if he picks a running mate who sits badly with Republican delegates already deeply split over his presumptive nomination.

Retired neurosurgeon Ben Carson, who initially led Trump's vice presidential selection process, stirred up GOP passions recently when he declared that he'd be "happy to talk to" a Democrat interested in the job, should that person meet his conservative criteria. Trump himself claims to have narrowed his short list of potential running mates to "five or six" people with experience in politics.

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Trump says he will announce his running mate in Cleveland. But while party conventions typically rubber stamp the nominee's vice presidential choice, Potter says, things may be different for Trump. Under convention rules, a majority of the delegations of eight states must formally nominate someone for vice president. Trump could undoubtedly rally enough delegates from eight states to nominate his choice.

But if a majority of delegates exist in eight other states to nominate an alternative running mate, they will be free to do so. Several thousand delegates will attend the Cleveland convention, many of them party operatives, local officials, and grassroots organizers with no allegiance to Trump and, in many cases, with strong antipathy to him.

"This is a real opportunity for people who are unhappy about these developments to have a role in the process, and effectively a veto power over who is chosen-and potentially an activist role embarrassing for the convention and the nominee if he gets his choice wrong when he's looking at things," says Potter.

Many of the Republicans first considered likely vice presidential picks for Trump have said flat-out that they would not consider serving as his running mate. These include Carson, South Carolina Governor Nikki Haley, New Mexico Governor Susana Martinez, and Florida Governor Rick Scott. Former Trump presidential rivals John Kasich, the Governor of Ohio, and Marco Rubio, the Florida Senator, have also ruled it out. Possible vice presidential contenders still in the mix include Tennessee House member Marsha Blackburn, former House Speaker Newt Gingrich, of Georgia, and New Jersey Governor Chris Christie.

The Cleveland convention could also feature floor fireworks over the GOP platform, which is likely to be contentious given Trump's ambiguous position on abortion, his opposition to free trade and his pledges not to cut Social Security or Medicare. Many delegates pledged to vote for Trump as the presidential nominee will feel no obligation under the rules to support his agenda when it comes to the party platform.

But the selection of Trump's running mate may prove the most important ace in the hole for Republicans upset over the divisive billionaire's role as their standard bearer. The first round of candidate balloting in Cleveland will presumably win Trump the nomination. But the next vote the convention takes will be for the vice presidential nominee. The wide-open rules for that process will force Trump to win the majority of convention delegates. He will not have a blank slate. Notes Potter: "I think it presents yet another complexity for Trump, and he's going to have to handle this very carefully."