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Gupta and Kumar (2000) showed that the throughput capacity of static ad hoc networks with n randomly positioned nodes is Θ(√(n/log n)). Grossglauser and Tse showed that node mobility increases the capacity to Θ(n), a substantial improvement. Achieving maximum capacity requires nodes to relay transmissions through other nodes. Each node must have a relay buffer for temporarily storing packets before forwarding them to their destination. We establish that if relay buffer sizes are bounded above by a constant, then mobility does not substantially increase the throughput capacity of mobile ad hoc networks. In particular, we show that the capacity of mobile networks with finite buffers is at most Θ(√n). Finally we establish a scaling law relationship that characterizes the fundamental tradeoff between throughput capacity and relay buffer size. In particular, we show that the throughput capacity is at most Θ(√(nbn)), where bn is the size of the relay buffers.