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By Phil LeBeau, CNBC

Americans overwhelmingly want to buy and ride in self-driving cars, but they do not want the "brains" of those vehicles to come from automakers, a new survey has found.

Automotive consulting firm AlixPartners surveyed more than 1,500 people between the ages of 18 and 65 and found that 73 percent would like a vehicle to do all of the driving. Yet when asked who they would trust more to program the car's software, 41 percent chose the experts in Silicon Valley. That compares with 26 percent who selected Japanese automakers, and 17 percent who opted for Detroit's Big Three.

Test drivers use a Lexus SUV, built as a self-driving car, to map the area prior to a journey without a driver in control, in Phoenix, Arizona April 5, 2016 in a photo provided by Google. REUTERS/Google/Handout via ReutersREUTERS

When it comes to building these vehicles, however, respondents said they have the most trust in the three major U.S. automakers — Ford, General Motors and Fiat Chrysler.

"People want the traditional automakers to be the brawn, building these cars, and they want tech firms to be the brains of the cars," said Mark Wakefield, head of the Americas automotive practice at AlixPartners.

The distinction is important because automakers and tech firms, who are investing billions to develop self-driving cars, have resisted forming partnerships. That's in part because they cannot agree on who will own the artificial intelligence, software and revenue streams coming from self-driving cars.

After Fiat Chrysler announced a partnership with Google to develop a test fleet of autonomous-drive minivans in May, FCA CEO Sergio Marchionne clarified that the deal was limited. When asked who would own the data collected by the self-driving vehicle, the executive said, "We need to get to a stage where the car is viable so we can discuss the spoils of that work. We're not there."

There have been rumors of other partnerships, but none have been announced.

Read More From CNBC: Face It, You're a Worse Driver Than an Autonomous Car

As automakers and tech firms race to develop self-driving cars on their own, AlixPartners' research indicates the players in Silicon Valley are winning in the minds of many consumers. When the research and consulting firm asked Americans to name a self-driving car, 42 percent said Google. The second most-common answer was Tesla, at 23 percent. The traditional automaker registering the highest score was Ford, at 5 percent.

"Consumers see Google and Tesla as being on the front line of autonomous-drive technology," Wakefield said.

It's easy to see why. Over the last two years there have been numerous news reports about the Google car driving around the Silicon Valley. Meanwhile, Tesla's autopilot technology allows drivers to take their hands off the wheel for short periods of time. Like the Google car, there is plenty video on the internet showing Tesla owners driving hands free.

But Wakefield said the public still sees a huge role for automakers in developing self-driving cars. In fact, 33 percent of consumers surveyed said they trust the Big Three most when it comes to providing the best value for a self-driving car. That compares with 18 percent who chose tech firms in Silicon Valley. Meanwhile, the Big Three also topped the list for whom consumers trust the most to build a self-driving car.

Wakefield said part of the discrepancy between customer preferences could boil down to automakers' spotty record with infotainment systems, which have become a top complaint among new car buyers.

"Infotainment systems in vehicles continually lag the performance of mobile phones," Wakefield said.