(b) That's wrong. In Australian law, companies are created by a process called 'registration' under the provisions of legislation called the Corporations Act 2001 (Cth). A body called the Australian Securities and Investments Commission (ASIC) maintains a register of all Australian companies. To create a new company, an application must be made in the proper form to ASIC and the required fees paid. If and when the application is accepted, the new company is entered onto the register of companies. An Australian Company Number (ACN) is issued to each company registered.
Of course, this is a simplified description of the process, and there are a number of formalities that must be complied with, but essentially (and depending on the circumstances) it is not difficult or expensive to create a company by registration.
It must be understood that a company created by registration under the Corporations Act 2001 (Cth) is one example of what is more generally called a 'corporation'. The word 'corporation' may be used to refer to any entity that is recognised in law as an artificial person. For example, it is possible to incorporate non-profit organisations, such as sporting associations or community service organisations, under the Associations Incorporation Acts of the states and territories. However, an association that is formed for trading or business purposes cannot incorporate under the Associations Incorporation Acts. Practically speaking, therefore, when we think of a corporation as a business organisation, we mean a company registered under the Corporations Act 2001 (Cth).