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Broadcasting allows efficient information sharing and fusion in wireless networks. In this paper, the energy efficiency limits in wireless broadcasting, defined as the minimal achievable broadcast energy consumption per bit (BEB), are studied. Specifically, we consider that a source node broadcasts information bits in a planar disk region A. And n relay nodes, which assist the broadcasting, are also placed in A. The limits are studied for both arbitrary and random wireless networks, under both non-cooperative and cooperative relay transmissions models. Closed form expressions are obtained. The results show that the minimal BEB, in general, decreases polynomially with n, and increases polynomially with the area of A. Cooperative relay transmissions offer at most a constant gain, in terms of the minimal BEB, over noncooperative transmissions, except for the free space propagation. As an example of application, our results are utilized in the study of wireless sensor networks, where the broadcast information fusion strategy is described and analyzed.