Stock Record
  
In the old days, if you bought shares of a company, you actually received a stock certificate. It was a physical paper document that showed your ownership of the shares.
Nowadays, these certificates are pretty rare. If you own shares, the proof that you own them comes from a digital record held with your broker. This list of stocks and their owners has a name: a stock record.
Each brokerage firm keeps a detailed stock record. It shows who owns what, and where the securities are being held. Each time shares are bought or sold, the brokerage firm updates the stock record.