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In this paper, we consider the transport capacity of ad hoc networks with a random flat topology under the present support of an infinite capacity infrastructure network. Such a network architecture allows ad hoc nodes to communicate with each other by purely using the remaining ad hoc nodes as their relays. In addition, ad hoc nodes can also utilize the existing infrastructure fully or partially by reaching any access point (or gateway) of the infrastructure network in a single or multi-hop fashion. Using the same tools as in [9], we show that the per source node capacity of Θ(W/log(N)) can be achieved in a random network scenario with the following assumptions: (i) The number of ad hoc nodes per access point is bounded above, (ii) each wireless node, including the access points, is able to transmit at W bits/sec using a fixed transmission range, and (iii) N ad hoc nodes, excluding the access points, constitute a connected topology graph. This is a significant improvement over the capacity of random ad hoc networks with no infrastructure support which is found as Θ(W/√Nlog(N)) in [9]. We also show that even when less stringent requirements are imposed on topology connectivity, a per source node capacity figure that is arbitrarily close to Θ(1) cannot be obtained. Nevertheless, under these weak conditions, we can further improve per node throughput significantly. We also provide a limited extension on our results when the number of ad hoc nodes per access point is not bounded.