Want to see your money grow as quickly as possible? Recent history suggests that mid-cap stocks, or those typically defined as having market caps of between $2 billion and $10 billion, are what you should consider buying. According to Morningstar, a hypothetical $10,000 invested on Dec. 31, 1995, would have been worth nearly $84,000 at the end of 2015, compared with $68,000 for small-cap stocks and just $48,250 for large-cap stocks.  

But which mid-cap stocks offer the best potential to see your investment grow into large-cap territory over the long run? For that answer we turned to three of our Foolish contributors, who wound up singling out specialty biotech Jazz Pharmaceuticals (NASDAQ:JAZZ), private-banking provider First Republic Bank (NYSE:FRC), and video-game publisher Take-Two Interactive (NASDAQ:TTWO).

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Don't sleep on this rapidly growing biotech stock 

Sean Williams (Jazz Pharmaceuticals): Though it's a company already bordering on large-cap territory, with a $9 billion market cap, specialty-drug maker Jazz Pharmaceuticals has, in my view, some serious large-cap aspirations.

Jazz, an Ireland-based drugmaker, leans heavily on its lead drug, Xyrem, a treatment for narcolepsy. Significant pricing power and an uptick in usage have been instrumental in growing sales of Xyrem throughout the years. During the first quarter, Jazz reported a 9% increase in year-over-year sales to $272.3 million and, on an extrapolated basis, puts Xyrem on track achieve blockbuster sales of near $1.1 billion in 2017. 

Jazz's pricing power on Xyrem and the possibility of generic competition have long been a concern of Wall Street, but I view neither as being particularly worrisome. In April, Jazz announced a settlement with Hikma Pharmaceuticals that allows Hikma to sell generic Xyrem beginning in 2023, which gives Jazz nearly six more years of high-margin sales for Xyrem without the fear of generic competition.  Similarly, the chances President Trump will successfully get drug-price curbs from Congress seem slim at best. With lawmakers focused on a new healthcare bill and tax reform, and Republicans in general favoring free-market economics, there's little reason to believe Jazz will see its pricing power on Xyrem negatively affected.

Jazz has also been working to diversify its product portfolio and pipeline away from its reliance on Xyrem. Sales of severe hepatic veno-occlusive disease treatment Defitelio doubled during Q1 to $35.9 million, and in April the company submitted a rolling new drug application for vyxeos as a treatment for acute myeloid leukemia. If approved, vyxeos could see sales approach $750 million annually at its peak, which would make its $1.5 billion acquisition of Celator Pharmaceuticals seem quite the bargain. 

With plenty of operating cash flow, strong margin, and lessening gray clouds, Jazz Pharmaceuticals has the potential to blow well past the $10 billion cutoff to be considered a large-cap stock.

A bank teller hands cash to a customer.

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The banker to the 1%

Jordan Wathen (First Republic Bank): This bank stretches the boundaries of the mid-cap definition, currently valued at about $15 billion, but it's almost certainly going to grow larger.

The company operates as a banker to the wealthy in key markets such as Silicon Valley, New York, Los Angeles, and Boston. It has 7% deposit market share in the San Francisco area and so has probably reached scale in Silicon Valley, but it has less than 2% share in Boston, and less than 1% in New York and Los Angeles. These metro areas present an excellent opportunity for growth.

Focusing on wealthy clients is an inherently good banking model, as the cost of maintaining a customer relationship doesn't necessarily scale with the value of the customer. High-net-worth borrowers make for excellent credit risks, which is reflected in the fact that it has charged off less than 0.5% of loans in each of the past 15 years. Management is a key part of the story here, as James Herbert has proved to be a capable deal-maker and manager.

The market has rewarded First Republic's underwriting quality and growth opportunity with a rich valuation, which recently stood at about 2.5 times tangible book value, or about 24 times last year's earnings. That said, core earnings power is growing each year at a breakneck pace, as deposits and loans have grown at more than 20% annually in the past 15 years, with little signs of slowdown.

If the market allows the valuation to adjust to 2 times tangible book value -- to account for a recent decline in interest rates -- it would make a fantastic addition to a growth-oriented portfolio.

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An explosive entertainment company

Keith Noonan (Take-Two Interactive): Video-game publisher Take-Two Interactive's valuation has exploded over the past five years, with its market cap increasing 750% over the stretch to reach roughly $7.8 billion. But the strength of the company's properties and momentum from industry trends suggests that growing into large-cap territory is in sight.

Take-Two has been benefiting from growth in digitally delivered content, which is doing great things for its sales and earnings and looks poised to continue boosting performance. Video-game players are increasingly downloading titles instead of purchasing physical retail copies, but they're also buying up in-game items, virtual currency, and content expansions at record levels, creating high-margin sales that look to become the new normal for Take-Two. The company is also benefiting from great engagement with its Grand Theft Auto and NBA 2K franchises, the latter one in particular, but there are notable growth avenues outside its core console video-game business.

The mobile market is one area that presents a huge opportunity for Take-Two. For the current fiscal year, the company expects just 6% of its sales will come from software on smartphone and tablet platforms, but comments from management and its recent purchase of mobile developer Social Point suggest that it aims to make much bigger inroads in the $41 billion mobile-games market.

If the company can continue to leverage its core franchises and benefit from digitally delivered sales growth, it has solid appreciation potential. If it also manages to introduce new intellectual properties with long-term staying power, while taking advantage of opportunities in areas such as mobile, esports, and mixed reality, then the high-flying video-game company still has huge long-term growth ahead.