A transfer agent for a publicly held company keeps records of stock held by registered shareholders, including shares held in certificate form. When stock changes hands, the transfer agent updates the record of ownership of the stock. The transfer agent does not maintain records of shares bought and sold through brokerage accounts and held in "street name." Such records are maintained by the specific brokerages through which shares are bought and sold.
The transfer agent is also responsible for escheatment, which is the legally-required process of transferring unclaimed property to the state. If you are a registered shareholder of Apple stock, it is critical that you maintain current contact information with the transfer agent; otherwise, you are at risk of having your shares escheated. If you hold your shares through a brokerage account, you should ensure that your address is current with your brokerage firm.
Apple’s transfer agent is Computershare Investor Services.