If a register exists, it is then usually the main evidence of ownership of the securities. It is more important than paper certificates. Certificates and other written evidence of ownership may be useful for trading, when tracing fraud or for tax returns.
It is also common for securities to be held by stockbrokers' nominee companies. The broker's clients who bought the securities are the beneficial owners. There are problems with this arrangement as these shareholders do not always receive the same rights (particularly to vote at AGMs and EGMs) as those whose names appear on the register.
Maintaining the register of shareholders is the responsibility of the company secretary. Most companies of any size find it more cost effective to outsource most of the actual work to a specialist registrar.