The chairman of the Republican Party in American Samoa, Utu Abe Malae, began feeling the pressure almost immediately: phone calls, commitment forms, anything the presidential campaigns could do, say or send to nail down his support as a delegate.

Ken Callahan, a district chairman for the North Dakota Republican Party, is perpetually fielding calls not just from the campaigns, but also from neighbors and friends who, excited by the process that is starting to unfold, are interested in becoming delegates themselves.

“I receive, I would say, 10 to 15 calls a day,” he said, “and it doesn’t stop on weekends, either.”

And Holland Redfield, a Republican delegate and former lawmaker in the Virgin Islands, had a special call-in guest on his radio program the other day: Gov. John Kasich of Ohio, who promised more than just lip service to the islands if he became president. After years of being treated like second-class citizens by mainland politicians, Redfield said, “we are in the catbird seat. There’s going to be some hard bargaining.”

Suddenly, they matter: For the first time in 40 years, the delegates to the Republican National Convention could be more than just a rubber stamp on their party’s nomination process.

The out-and-out wooing has not yet begun. But it seems only a matter of time before campaigns start using all the trappings of prestige, power and who-knows-what-else they are able to muster.

“There are a lot of delegates who’d like to ride on Trump’s plane,” said Roger Stone, a friend and informal adviser to Donald J. Trump. “There are a lot of delegates who’d like to have a phone call from Ivanka Trump. We’ll get to that phase.”

Experts on the nominating rules said that restrictions on what delegates can accept vary by state but are generally quite permissible. For instance, nothing prevented President Gerald R. Ford from using flights aboard Air Force One to charm delegates in 1976.

The task of herding and cajoling 2,472 men and women spread out across two oceans and 10 time zones is an immense and intricate undertaking that few in the political world have any experience participating in — let alone managing.

It is a process that can seem far removed from the way most Americans think presidential nominees are selected: Small gatherings of obscure county and state leaders can overrule the popular will of voters. Few ethical or legal constraints govern how delegates can be courted. And outposts like Guam or the Virgin Islands could have just as much say as Iowa or New Hampshire in picking the nominee, because of the unusual way in which some states and territories have permitted their delegates to act as roving free agents.

So few political operatives know how to navigate the conflicting loyalties, competing interests and arcane procedures involved, a seller’s market has sprung up for anyone with convention experience.

“There aren’t many people who know this stuff,” said Jason Osborne, an expert on Republican procedures who has advised several presidential campaigns this year. “You can read up on it. But unless you’ve been through a convention and understand how quickly things can move and change, you’re at a disadvantage.”

Trump, who has been loath to embrace many of the tools of modern political campaigns in his run for the presidency, has brought on a parliamentarian to master the intricacies of party rules.

Sen. Ted Cruz of Texas has cultivated ties to individual delegates from Virginia to Guam, aware that every last vote could count.

And Kasich has signed on aides who were involved in the Republicans’ last contested convention, in 1976, when Ford prevented Ronald Reagan from forcing a second round of voting, which most likely would have ended in Ford’s defeat.

The procedural peculiarities of the nominating process this year are adding a new twist. All 50 states, plus the five territories and the District of Columbia, have a vote, but several states and territories have given themselves outsize influence by allowing their delegates to act as free agents.

The biggest slate yet of totally uncommitted delegates will be selected in North Dakota over the weekend at the state’s Republican convention in Fargo. As a sign of its importance, Ben Carson, the retired neurosurgeon who quit the race last month, will campaign there on behalf of Trump, whom he has endorsed. Cruz plans to appear himself.

Uncommitted delegates are free to decide whom they will support. They can promise allegiances or switch at will, operating with no constraints binding them to the outcome of a statewide primary. And they can do so individually, or as a bloc, if they seek to exert more power: Almost all of them, after all, come from places that have had little or no influence in presidential elections, like American Samoa, Guam, the Virgin Islands and North Dakota.

“We want to be able to change our minds,” said Malae, the American Samoa Republican Party chairman.

Being uncommitted and unbound, Malae said, was precisely the point for a place like his territory, which has no vote in Congress or in the Electoral College.

“We joke that this must have been what it was like being in an outpost of the Roman Empire,” he said.

All told, there could be several dozen totally uncommitted delegates on the convention floor in Cleveland, a tiny fraction of the 1,237 needed to clinch the nomination, but enough to swing a close race.

At the state conventions in Colorado and Wyoming, for instance, participants will be able to choose from among bound and unbound delegates, potentially adding to the total of free agents. And a lawsuit in the Virgin Islands could lead to some delegates’ being bound to Cruz and Trump, though all nine of the territory’s delegates were elected as uncommitted at a March 10 caucus.

“The most important delegations at a contested Republican National Convention,” is how John Yob, a Republican strategist regarded as a process savant who has worked for several presidential campaigns, has characterized these untethered power players.

Yob, who also happens to be one of the disputed unbound delegates from the Virgin Islands, became so fascinated with the machinations involved that he wrote a book that is intended to serve as a primer on the process. The title, “Chaos: The Outsider’s Guide to a Contested Republican National Convention 2016,” looks more prescient every day.

The state contest in North Dakota this weekend, followed by the gatherings in Colorado and Wyoming over the next two weeks, will determine many of these delegates.

Demand to be a delegate is as high as it has ever been. Carma Hanson, vice chairwoman of the North Dakota Republican Party, said she had to get in line for one of her state’s 28 delegate spots: There were four applicants for each opening.

Even her husband and son wanted in on the action. They applied to be alternates.

“It could make for a very interesting convention in July,” she said. “And people want to be a part of that.”

It is unclear if the surge of interest will benefit any particular candidate. In North Dakota, Republican officials are screening delegate applicants in hopes of elevating those who have a history of volunteering for and donating to the party. That would not seem to benefit Trump, though voters at the convention will have the final say.

In Colorado there is no such screening. Steve House, the state Republican chairman, said that in his informal surveys of the dozen or so county assemblies he has attended — gatherings where delegates to the state convention were selected — about 40 percent of the people told him it was their first time participating.

“There’s a fair amount of new people, without question,” House said.

Malae of American Samoa said that in any other year, he would have had a hard time finding delegates. It is a commitment that comes with a price. Travel from the remote territory in the Pacific, through Honolulu, to the convention in Cleveland will cost around $6,000.

This year, however, there was so much local interest in becoming a delegate, Malae said, that all nine delegates had already put down deposits so they would not lose their places.

© 2016 The New York Times Company