The launch of the more affordable Model 3 is set to propel the global fleet of Tesla (TSLA) - Get Report vehicles on the road by three times by the end of 2019, Morgan Stanley analysts said in a note Tuesday.

The on-road population of Tesla vehicles will reach 300,000 by the end of this year, rising nonlinearly to as many as 32 million units, or 107 times the current Tesla population, by 2040. "It has been generations since the investment community witnesses such a high growth rate in the population of a single auto firm," analysts wrote.

As Tesla cars become more ubiquitous, the Model 3 could lead the charge. "You'll probably see this car every day throughout the day within a couple of years," analysts noted. Tesla is set to capitalize on word-of-mouth advertising for the Model 3, just as it did for the Model S.

With such a boom in on-road population, Tesla's "investment in charging and service infrastructure will be put to the test," Morgan Stanley added. But Tesla has made the largest proprietary investment in superchargers and destination chargers of any firm in the world. In some places, the charging network is even bigger than it needs to be as Tesla anticipates rapid growth.

With such exponential growth comes risks, Morgan Stanley noted. Quality and safety risks are "a fact of life in the auto industry." If Tesla can continue to deliver high quality products, it will increase its pull with new customers and capital.

Morgan Stanley rates Tesla "equal weight," with a $317 price target.

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