According to the newest available data, Tesla holds an 18% market share of the electric car market globally. With the global electric market growing on a daily basis, that number could change very quickly.
Right now, it seems like Tesla is a big fish in a very little pond spending years leading the electric vehicle market. With its large volume production, its Model 3 and Model Y leading EV sales all over the world, and the Model S and Model X beating several other vehicles when looking at volume, Tesla is the one to beat. (via EV Sales Blogspot):
As seen in the table, Tesla currently holds about 18% of the global electric vehicle market to date. Volkswagen come second to the California-based company but still only holds about a third of the volume Tesla does. However, these numbers will inevitably change as more than a dozen new electric vehicle programs are expected of the course of the next year, and we can only assume many more will follow.