There is no registration requirement for a general partnership in New York, so whether one exists is a question of fact decided by this section's four rules. Rule 1: except as provided by § 27, persons who are not partners as to each other are not partners as to third persons. Rule 2: joint tenancy, tenancy in common, tenancy by the entireties, joint property, common property or part ownership does not of itself establish a partnership, whether or not the co-owners share profits made by use of the property. Owning something together is not being in business together. Rule 3: sharing gross returns does not of itself establish a partnership, whether or not the people sharing them have a joint or common interest in the property producing them.
Rule 4 is the one most cases turn on. The receipt by a person of a share of the profits of a business is prima facie evidence that he is a partner in the business. Net profits, not gross returns - the distinction between rules 3 and 4 is deliberate, and a share of the takings is not the same as a share of what is left after expenses.
The rule then lists five payments from which no such inference is drawn: profits received as a debt by installments or otherwise; as wages of an employee or rent to a landlord; as an annuity to a surviving spouse or representative of a deceased partner; as interest on a loan, even where the amount varies with the profits; and as consideration for the sale of the goodwill of a business or other property, by installments or otherwise. Those five cover most of the arrangements that look like partnership and are not - the profit-sharing employee, the landlord on a turnover rent, the lender paid out of profits, the seller taking an earn-out.