Place your bets: The race to find the next Tesla is on — but the search is turning up plenty of clunkers as well as potential superstars.

Fidelity Investments, BlackRock Inc., T. Rowe Price Group Inc. and Scotland's Baillie Gifford are among the fund houses helping to bankroll the shift from fossil-fueled transportation, with investments in one or more of 32 electric vehicle industry companies they believe will be long-term winners in the electrification movement.

In the short term, there have been some bumps in the road.