NEW YORK (TheStreet) -- Now that Ferrari is going public, will the luxury brand be forced to increase its production?

The famed automaker recently filed papers for an initial public offering in which Fiat Chrysler (FCA) - Get Report, Ferrari's primary owner, will sell 10% of the company to the public. Eighty percent of Fiat Chrysler's remaining shares will be distributed to existing Fiat Chrysler shareholders. The rest of Ferrari -- 10% -- will remain in the hands of Piero Ferrari, son of company founder Enzo Ferrari.

But despite the speculation, there's one area of the business that's sure to remain as exclusive as ever: its custom build program for one-off, totally original cars. 

"This is a private portion of their business," said Stephen Reitman, an auto sector researcher at Societe General. "We don't have any of the numbers for it, but we know it's incredibly profitable."

Here's a look at some of the rarest vehicles, built both for racing purposes and on personal whim, from one of the world's most restrictive car makers.

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1. The "Breadvan"

While nicknamed for its resemblance to a common English delivery truck, the Ferrari 250 GT SWB, affectionately known as the "Breadvan," was built as a proof of concept for the aerodynamics of the "Kamm tail," now a common auto body style with an abruptly chopped-off back. Built in 1962, the design went on to set a course record on the notable Ollon-Villars circuit in Europe, reaching a top speed of 62 miles per hour on an uphill mountain road.

A longtime devotee of the brand, Eric Clapton realized his own vision of Ferrari perfection in 2012 when he commissioned the SP12 EC as part of the Tailor-Made customization program. The price? A cool $4.7 million.

According to the Tailor-Made website, clients of the program "make their personalization choice on site in Maranello [Italy] where they are flanked by a personal designer who will assist them in creating their bespoke Ferrari right down to the tiniest detail."

Despite initially wanting a V12 engine for his masterpiece, Clapton was eventually persuaded by the manufacturer to accept a more modest V8.

3. The King Leopold Ferrari

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Famed industrial designer Battista "Pinin" Farina designed this 375 Plus Cabriolet for King Leopold III of Belgium after he abdicated the throne in 1950. Finished in 1954, the car originated the headlight and body contours that would come to define the popular Spyder models years later. After the monarch had his fun with the Cabriolet, it became the object of an intense contractual dispute between wealthy Americans that ultimately reached the U.S. Court of Appeals. In 1985, it failed to change hands for an agreed-upon price of $275,000.

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4. The Navarro Special

It's hard to conceive of why anyone would want to modify a stock 330 GT to look like a 1970s Chevy hatchback, but such was the proclivity of Italian nightclub owner Norbert Navarro, who in 1966 augmented his Ferrari with sparkly gold paint and tail fins. Legendary for its aesthetic departures from the brand's iconic look, the Navarro Special, as it's come to be known, was actually designed by renowned auto fabricator Piero Drogo, who has fetched record prices at auction for his custom collaborations with the Italian carmaker. The Navarro Special, however, has never been among them: One commentator puts the value of the car at $400,000, chump change for a one-of-a-kind prancing pony.

5. The Testa D'Oro 

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The customized Ferrari Testa D'Oro Colani, which went on sale in Italy in June for $1.7 million, was built to break speed records at the Bonneville Salt Flats. It accomplished that goal for its class in a 1991 trial, reaching a top speed of 220 miles per hour. While the outlandish body design is unofficial and belongs to Luigi Colani, Ferrari did make special modifications to the engine to help it reach its speed objectives, including catalytic converters and two superchargers. Remarkably, a Facebook page for the car claims that it's street-legal in Germany.