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We study the scaling of the broadcast capacity for a network with a single source and f(N) cooperative relays where N is the number of destinations and f(.) is an increasing function. We consider random extended networks (the network area goes to infinity while the node density is fixed). In this asymptote, we show that the broadcast capacity is upper bounded by Theta(1) when path-loss exponent is greater than 2. We provide a multistage cooperative broadcasting scheme which achieves the same scaling as this upper bound. A continuum approximation for the network is utilized in order to obtain this result.