No, you don’t. With Vivid Invest we offer trading in relation to Fractional Shares. It is technically not possible to co-own a stock.
Fractional Shares are one-to-one bilateral agreements (derivative contracts) with specific stocks or ETFs as underlying. The Fractional Share performance is fully linked to the price development of the underlying asset. There is no leverage.
For more information check “What is the nature of Fractional Shares?”.