The millionaires, billionaires and companies giving big sums to political committees supporting Mitt Romney, Newt Gingrich and President Obama have important business with the next president. Some are in trouble with the government and could use a sympathetic ear in the White House. Some are pressing for new laws or regulations that would benefit their interests in energy, mining and high finance.

The Associated Press reviewed financial reports, regulatory filings, court records, public statements and more to identify favors that the biggest donors so far in the presidential campaign might want in return for their contributions worth $100,000 or more. In some cases, these donors have given $1 million or more to help Obama’s challengers or the president.

An exhaustive review of their motives is nearly impossible, since new federal rules governing such contributions allow donors to effectively remain anonymous if they funnel cash into the campaign through corporate partnerships or other mechanisms that can frustrate an investigation.

The presidential campaigns all have said they do not trade political favors for election money.

Among AP’s findings:

• An energy firm run by William Koch, a $1 million donor to the pro-Romney political committee, paid to lobby Congress on mining and safety issues and also over a proposed federal land swap that would enlarge the donor’s Colorado ranch.

• The casino company run by Sheldon Adelson, the billionaire whose family has given $11 million to a political committee that supports Gingrich, has acknowledged it’s under federal investigation by the Justice Department and is the object of a civil probe by the Securities and Exchange Commission for possible violations of the Foreign Corrupt Practices Act. The company denies wrongdoing and says the investigation stems from an allegation by a disgruntled employee. Adelson’s family has provided nearly all the money that the pro-Gingrich group has received so far.

• A hedge fund run by a New York investor, Paul Singer, who gave the pro-Romney group $1 million, has pushed for federal laws that would give official U.S. backing to the firm’s legal efforts to profit from the debt of distressed and Third World nations.

• A board member and former chairman of a prestigious Los Angeles hospital, John C. Law with the Cedars-Sinai Medical Center, has given the pro-Obama committee $100,000 as the hospital has lobbied Obama’s administration over Medicare and Medicaid funding for teaching hospitals and electronic medical records, the National Institutes of Health and Army research programs.

• A Pennsylvania coal producer, Consol Energy Inc., which donated $150,000 to the pro-Romney group, paid a $5.5 million fine last year for violations of the Clean Water Act at six of its mines. It is lobbying to prohibit the federal government from regulating greenhouse gas emissions. Weeks after the company gave money to support Romney, who previously had agreed that humans are contributing to climate change, the candidate appeared to back off that position and said he would oppose spending high amounts of federal money to reduce carbon dioxide emissions, like those from coal plants.

The high-dollar contributions have flowed into the presidential campaign through so-called super PACs, which can support a specific candidate but can’t lawfully coordinate their spending with a candidate’s campaign. The groups, given a green light by the Supreme Court in 2010 when it stripped limits on corporate and labor union spending in elections, have already proved to be strategically successful for candidates. The pro-Romney group, Restore Our Future, spent $8.8 million on ads in Florida alone — more than Romney’s own campaign — and has already booked TV spots in Arizona, Michigan and Minnesota.

A Romney campaign spokeswoman, Andrea Saul, dismissed any suggestion that wealthy donors are motivated by their private interests to fund the committee’s operations.

“To the degree Americans support Mitt Romney,” she said, “it’s because he can reverse the decline of the Obama economy and get Americans back to work.”

Obama so far has fewer big-money donors. He is able to marshal the resources of the Democratic National Committee, and it is typically easier for incumbents to raise money closer to the November election.

Public-interest groups have warned since the Supreme Court ruling that wealthy individuals, corporations, unions and other interests would seek favors in return for unlimited campaign contributions.

“The size of these donations counts for a lot, and the candidates will naturally be grateful to these organizations and their donors,” said Sheila Krumholz, executive director of the nonpartisan Center for Responsive Politics in Washington. “And with greater support, comes increased gratefulness.”