1) The true test of partnership is the existence of "mutual agency", where each partner has the ability to bind the other partners through actions taken in the name of the firm.
2) Sharing profits is a prima facie evidence of partnership but not a conclusive proof on its own.
3) A partnership agreement should ideally be in writing to avoid disputes, and is called a partnership deed. The deed outlines important terms like the name of the partners, nature of business, capital contributions, profit/loss sharing, and circumstances around retirement, expulsion, death, or dissolution.