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The benefits of infrastructure support are shown by analyzing a capacity scaling law of an erasure network in which multiple relay stations (RSs) are regularly placed. Based on suitably modeling an erasure probability under the network, we first derive a cut-set upper bound on the total throughput. Our result indicates that the upper bound depends on the number of RSs but not on the erasure probability. We then show our achievability based on two existing multi-hop transmissions with and without help of RSs. It is shown under the RS-supported erasure network that the achievable scheme is order-optimal for all the network conditions.