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We study the benefits of opportunistic routing in wireless networks by examining how the power and delay scale as the number of source-destination (S-D) pairs increases, where S-D pairs are randomly located over the network. The scaling behavior of conventional multi-hop transmission that does not employ opportunistic routing is also examined. The results indicate that the opportunistic routing can exhibit better power- delay trade-off than the conventional routing while providing up to a logarithmic boost in the scaling law. The gain comes from the fact that the system with opportunistic routing can tolerate more interference due to increased received signal power from utilizing the multi-user diversity gain. Furthermore, we derive an upper bound on the total throughput using the cut-set theorem. It is shown that the achievable rates of the conventional and opportunistic routing schemes become close to the upper bound when the number of S-D pairs is large enough.