In the US, if one buys shares of some company, say Apple, through some broker, say Charles Schwab, does one actually become an owner of the company (Apple in this case)? I used to assume this was the case until I discovered that when one chooses automatic dividend reinvestment, the broker will credit fractional shares to one's account. However, there is no such thing as fractional shares. Presumably, the broker owns the shares and keeps a record of who "owns" fractions. That is, from the point of view of Apple, the broker is the owner of the full share. Hence, could it be that this is always the case, regardless of whether we are dealing with full or fractional shares?
Please note, this is not a question about who "holds" or keeps record of the shares, not even about who has particular rights (like voting rights etc.), but rather a question about who has direct legal ownership of the company the shares reference. Who does Apple think their owner is?
What would be the situation in case of an ADR?
I would appreciate if someone could provide authoritative references.