FORTUNE — As Europe wallows in economic doldrums, at least one native son is thriving. Germany’s Volkswagen AG, which has its sights set on becoming the world’s top auto firm before the decade is out, is making headway. Across a broad range of businesses, the company’s aggressive expansion plans are bearing fruit and the Greek dynamics of the firm’s controlling families have settled down. The woes of its global rivals haven’t hurt, either.

VW is already global champ of the bottom line, with an operating profit of nearly $15 billion last year and a goal to match that amount this year. Martin Winterkorn, chief executive, said “the unbroken automotive boom is providing additional tailwinds for our growth plans,” referring to stronger sales in emerging markets, rather than in Europe where auto makers are struggling. Winterkorn drew a salary of 17.5 million Euros ($22.8 million) in 2011, more than double the year before — and more than any chief executive of all companies listed on the DAX, Germany’s main stock index. VW sold 8.27 million vehicles globally in 2011, up from 6.29 million the year before.

Most immediately, VW isn’t backing down from a promise to double production this year at its Slovakian factory in Bratislava. The chief executive of the automaker’s Volkswagen Group said on Wednesday that production will rise to more than 400,000 vehicles this year, compared to just over 210,000 last year. The plant used to build only large SUVs, but production is expanding thanks to the company’s new Up minicar. The Up was shown as a variety of concept vehicles since 2007, before going into production last year. It could expand into a sub-brand of smaller, eco-friendly vehicles much like Toyota’s (TM) Prius hybrid line.

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VW has become that rare species of automotive giant that can generate profits in disparate markets, from barebones hatchbacks popular with college freshman to the uber-tony Bentley, vehicle of choice for billionaires’ wives. The Volkswagen Group now owns Audi, Bentley, Bugatti, Lamborghini, SEAT, and Škoda as well as the truck manufacturer Scania. It has a 49.9% stake in Porsche. “VW has shown it can build the right cars for the right market at the right price,” says Jesse Toprak, vice president of market intelligence for TrueCar.com, an automotive website. “It has a whole building full of people in Wolfsburg that do nothing but optimize pricing – and they’re very good at it.”

Audi, VW’s mainline luxury-car subsidiary, is another bright spot. Long regarded as an also-ran in America, it has undergone a remarkable turnaround and seen sales surge. Earlier this month, it pulled forward its volume target, predicting it will sell 1.5 million vehicles before 2015. Outside of the U.S., Audi is benefiting from strong demand for luxury cars in China, India and Russia. Better yet, Audi overtook Mercedes-Benz as the second-largest premium brand by vehicle sales last year. And though it still sells fewer vehicles than BMW, it flew past its main rival in terms of profitability thanks to the economies of scale its parent makes possible. (BMW, by contrast, is an independent company.)

Now, Audi is negotiating to buy premium Italian motorcycle manufacturer Ducati. Ownership of Ducati would add another powerful brand in the company’s duel with BMW, which manufactures luxury motorcycles under the same name. In the parlance of enthusiasts, bimmers are BMW cars and beemers are BMW motorycles. Ducati, a favorite of actors Tom Cruise and Brad Pitt as well as real estate titan Sam Zell, would bring some of that zeal to Audi. Founded in 1926, Ducati won 17 manufacturer’s World Championships in the past 60 years and the 2011 World Superbike Championship title. Its smaller engine technology could also provide a strategic benefit to Audi.

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VW’s weakest presence is in the U.S., where it has lagged due to a series of management and strategic mistakes. But that could be changing with the opening of a new plant in Chattanooga, Tennessee, where the company is building its new VW Passat midsize sedan. “The US is an anomaly for VW,” said Toprak. “The company has aspirations to raise its sales here to half a million this year. They’re being very aggressive.”

And then there’s the family. Controlled by the Porsche family, with roots in Germany and Austria, VW has hit its stride under the leadership of its chairman, Ferdinand Piech, a grandson of Beetle designer and VW founder, Ferdinand Porsche. Piech, 74, is known in the automobile industry as an exacting, demanding and uncompromising engineer – whose minions quake in their boots when he inspects their work. VW shares trade publicly; the family has control via a super-voting stock.

At the VW annual meeting on Monday, the supervisory board nominated another Piech to join it, Ursula, 55 who is Ferdinand’s wife. A former nanny to the Piech family, she is the mother to three of his 12 children. The VW empire is trying to resolve a bitter and complicated feud over control between Ferdinand and another grandson, Ferry Porsche, who tried to take over VW, using the much smaller Porsche company as his base. The tables were turned after the 2008 financial crisis when VW rescued debt-laden Porsche and bought a controlling stake.

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If Ursula Piech seems an unlikely figure on VW’s board — the company has described her as a kindergarten teacher — she is seen by some as playing peacemaker among the hostile family factions. VW, against expectations, may ultimately have benefitted from the animosities within the family. The carmaker’s current chairman came to VW as a career alternative when Ferry Porsche, founder, banned him and other Porsches from the sports car company. Now, with the VW Group pushing ahead, Piech looks fulfilled in what he once listed as his three great loves: “Volkswagen, family and money.”