By Michael Flaherty and Paul Lienert

(Reuters) - Investors questioned a plan by Silicon Valley heavyweight Elon Musk for his electric car company Tesla Motors to buy his rooftop solar company SolarCity for up to $2.8 billion, sending Tesla's shares down more than 10 percent on concerns the two would not fit together and a deal would distract Tesla from making cars.

However, there were signs that some of the biggest funds holding shares of both companies might be open to a deal.

Musk, an audacious entrepreneur who is the chairman of SolarCity Corp <SCTY.O>, chief executive of Tesla Motors Inc <TSLA.O> and the largest shareholder of both companies, envisions a one-stop shop for clean-energy fans, who would be able to buy an electric car, home solar system and battery backup in a single visit.

But many investors and analysts focused on practical concerns of the plan and whether Musk was giving himself a good deal.

Musk, who is also the CEO of rocket-maker SpaceX, and Tesla management risked being distracted from rolling out the new Model 3 sedan, a mass-market electric vehicle key to the success of the young firm, analysts said, questioning whether merging two companies which both need substantial cash was a good idea.

“Tesla’s double-down on solar energy raises important questions on strategy, capital adequacy and governance. Is the increased risk worth the potential reward?” Morgan Stanley analysts asked in a research note issued Wednesday.

FIDELITY FANS

In a hastily arranged call with investors and Wall Street analysts early on Wednesday, Tesla executives defended the deal, and said shareholders of both companies would likely vote on it in a matter of months. Musk, who owns about a fifth of each company, will recuse himself, leaving the fate of the deal in the hands of outside investors, led by major fund companies such as Fidelity Investments.

Some of those major investors, like Musk, hold shares of both companies.

Musk said on Wednesday that he had not told institutional investors about the deal in advance, but over the years, he said, "this idea has been bandied about with some of our largest shareholders, institutional shareholders. Yeah, there have been discussions."

The manager of the second largest mutual fund investor in Tesla, the $12 billion Fidelity OTC Portfolio, which is also the largest institutional holder of SolarCity, praised a tie-up in comments earlier this year.

“We remain fans not just of Tesla products, but of the concepts and potential future partnerships behind the company. We foresee fruitful synergies between say, Tesla and SolarCity – or any company that can benefit from superior battery technology,” Gavin Baker, who runs the Fidelity OTC fund, said in his first-quarter commentary for investors.

Baker and Will Danoff, who runs the $100 billion-plus Fidelity Contrafund <FCNTX.O>, the largest mutual fund investor in Tesla, have both told Reuters in interviews that they tend to give more leeway to founder-run companies which they believe are still in the early stages of growth.

Musk himself said that Tesla, now valued at less than $30 billion after Wednesday's stock fall, could be a trillion-dollar company one day.

"I have no doubt about this - zero," Musk said on the call with analysts and investors before markets opened on Wednesday. "We should have done it sooner."

Tesla on Tuesday offered to buy SolarCity in a stock deal worth as much as $2.8 billion.

Shares of Tesla were down more than 10 percent at $196.75 on Wednesday, putting its market value around $28.8 billion, down more than $3 billion from the day before. The much smaller SolarCity was up about 5.8 percent at $22.45, valuing the U.S. market leader in residential rooftop solar panels at about $2.2 billion.

Both Tesla and SolarCity have relied on regular fund-raising to underwrite expansion plans. The proposed merger had "little in the way of synergies (and) much in the way of cash burn," with "uncertain growth/cash prospects" for the combined companies, Barclays Capital auto analyst Brian Johnson said in a note.

Musk said SolarCity would post positive cash flow in the next three to six months and would not have a material impact on Tesla's future cash needs or expectation to be cash-flow positive by year-end. Costs for both companies would go down significantly after the merger, he said, without giving specifics.

The CEO, an engineer with a cult following approaching that of Apple's Steve Jobs, was the chief proponent of the deal in calls with reporters and analysts since it was announced, even though he will not vote on the transaction.

SolarCity shares have fallen more than 50 percent this year in a highly competitive market, fanning criticism that a Tesla deal was meant to save SolarCity.

"The brazen Tesla bail-out of SolarCity is a shameful example of corporate governance at its worst," short-seller Jim Chanos of Kynikos Associates said in a statement. The Tesla CEO recently sold stock, he noted. "It is hard for me to believe that this deal was not being contemplated when Tesla, and Mr. Musk himself, sold shares just a few weeks ago."

Tesla was not immediately available for comment but has said the share sales were to pay income taxes when Musk exercised options to buy shares.

Share lending data suggested short sellers were increasing their bets against both companies. Interest rates to borrow Tesla shares rose to 5 percent on Wednesday from 1.5 percent early in the day, according to S3 Partners, a financial analytics firm. Hardly any SolarCity shares were available for borrowing.

Charles Elson, finance professor and corporate governance chair at the University of Delaware, said that the creation of a special committee of independent directors is the usual response to a deal where board member conflicts may arise.

But even then, Elson said, a non-independent director who is both a founder and a major shareholder can wield a lot of influence.

"Any time a director is on two sides of a transaction, it raises questions. You have conflicting fiduciary duties, and, like any transaction, someone is going to get the better end of it," he said.

(Reporting by Supantha Mukherjee and Narottam Medhora in Bengaluru and Paul Lienert in Detroit; Additional reporting by Michael Flaherty, Alexandria Sage, Tim McLaughlin, Ross Kerber, Rishika Sadam and Noel Randewich; Writing by Peter Henderson; Editing by Anil D'Silva, Lisa Von Ahn and Bill Rigby)