Roughly speaking the way the US stock market works is that all of the stocks are in one place. The place is called DTC, the Depository Trust Company, which in some sense owns almost all of the stocks. If you own a stock, what you own is an entry on a list at your brokerage, saying that you are entitled to some of the stocks that it is holding onto for clients, and what your brokerage has is an entry on a list at DTC, saying that it is entitled to some of the stocks that DTC is holding onto. (And what DTC mostly owns is entries on lists at all the companies, or their transfer agents, saying that it owns the stocks that those companies issue.)