(a) That's right. In Australia, the law that regulates partnerships has been largely codified in state and territory legislation.
This legislation is, for all practical purposes, uniform across all jurisdictions as regards general partnerships. In New South Wales, Queensland, South Australia, Tasmania, Victoria and Western Australia the legislation also makes provision for limited partnerships (see pages 5.18 - 5.20 in this section).
The legislation describes how partnerships are created, what different kinds of partnership are possible, what legal rights and powers partners have; how a partnership is managed; what liabilities the partners have to each other and to third parties; and how partnerships are ended.
The partnership legislation allows partners to agree on the particular arrangements that may suit them, for example, the extent to which each partner must contribute to the partnership, or how the profits of the business will be shared between them. But in the absence of such agreed terms, the legislation provides residual rules.
In addition to the legislation there is, of course, a body of case law on partnerships.