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Cooperative broadcast aims to deliver a source message to the whole network by means of collaborating nodes. Critical parameters that influence the broadcast performance include source/relay transmission powers and the decoding threshold (the minimum SNR required to decode a transmission). We study the effect of these parameters on the number of nodes reached by cooperative broadcast. In particular, we show a phase transition behavior: if the decoding threshold is below a critical value, the message is delivered to the whole network. Otherwise, only a fraction of the nodes are reached proportional to the source transmit power. Our approach is based on the idea of continuum approximation, which yields closed-form expressions accurate when the network density is high.