Tesla Motors is one of several automakers planning to put a self-driving car on sale sometime in the next few years, and it already seems to have at least one big fan.

This person isn't a celebrity owner or safety advocate, but rather the CEO of preeminent ride-sharing company Uber.

If Tesla can build a fully-autonomous car by 2020, Uber CEO Travis Kalanick says his company would it. In fact, he'd buy every one Tesla builds.

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Yes, all 500,000 electric cars Tesla expects to produce in that year, according to Forbes (via Charged EVs).

That boast comes not directly from Kalanick himself, but from Steve Jurvetson--an early Tesla investor and board member.

Jurvetson relayed what he claimed were Kalanick's remarks at the recent Top 10 Tech Trends dinner, hosted by the Churchill Club.

UberCab app

He used his speaking time there to extol the virtues of autonomous cars.

"I believe they are already safer than my parents," he said, "and I would trust my kids with them."

He claimed that autonomous driving could significantly reduce the number of taxis on New York City streets, and still allow patrons to get a ride within 30 seconds of hailing one.

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Those benefits are of course theoretical and dependent on a number of variables--including Tesla's ability to meet its autonomy and production-volume goals.

Tesla CEO Elon Musk previously said he expects the company to build 500,000 cars per year by 2020.

That prediction was reconfirmed by Tesla chief technical officer JB Straubel at a conference in Washington, D.C. last month.

London anti-Uber taxi protest: June 11, 2014 (photo by Flickr user David Holt)

This would bring Tesla's cumulative output to 1 million vehicles by that point.

But will any of those vehicles be able to drive themselves?

Tesla has been building cars equipped with hardware for the first phase of its "autopilot" autonomous technology since last fall, although the system still isn't available to consumers.

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Initially, cars will be able to pass other vehicles with no involvement from the driver other than the flick of a turn signal.

Musk has said that Tesla plans to develop the technology to the point that a car can be summoned from a garage to meet its owner.

Tesla Model S P85D, 2015 Detroit Auto Show

Tesla may not offer this technology on all of its models, though.

By 2020, much of Tesla's sales volume will consist of the Model 3, a 200-mile electric car priced at $35,000 before any incentives.

The lower price point may mean Tesla will skimp on features like autonomous driving.

That would mean Uber would take delivery of somewhat fewer Tesla cars, but still an impressive amount.

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