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We study the capacity of random wireless ad hoc networks when nodes are capable of multi-packet transmission and reception (MPTR). This paper extends the unified framework of (n, m, k)-cast by Wang et al. for single-packet reception (SPR) at each node to the case of MPTR. (n, m, k)-cast considers all types of information dissemination including unicast routing, multicast routing, broadcasting and anycasting. In this context, n, m, and k represent the total number of nodes in the network, the number of destinations for each communication group and the actual number of destinations that receive the packets, respectively. We show that the capacity of a wireless ad hoc network of n nodes in which nodes have a communication range of r(n) and engage in an (n, m, k) -casting scales as Θ(n√(mr3)(n)/k), Θ(nr2(n)/k) and Θ(nr4(n)) bits per second when m = O(1/r2(n)), Ω(k) = 1/r2(n) = O(m) and k = Ω(1/r2(n)), respectively. We show that the use of MPTR leads to a gain of Θ(logn) compared to the capacity attained with multi-packet reception (MPR), and to a gain of Θ((logn)2) compared to the capacity attained with SPR, when Ω(√(logn/n)) = r(n) = O(√(loglogn/3logn)).