Illustrative example
Two friends ran a market stall together for three years, split the takings after costs and shared the work. After a falling-out one of them says it was always his business and the other was only helping out.
The definition needs no written agreement, no registration and no declaration: it is the relation subsisting between persons carrying on a business in common with a view of profit. The fact that decides which of the two accounts is right is 'in common' - whether the business was carried on by or on behalf of both of them, which shows up in who bore the losses, who dealt with suppliers and whose name was on the pitch, rather than in what either now says about it.
They agree the stall was a partnership from the first season, that stock and the trailer are shared equally, and that one buys the other out at an agreed figure with the takings from the current season split as before.