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This paper investigates the fundamental performance limits of medium access control (MAC) protocols for particular multihop, RF-based wireless sensor networks and underwater sensor networks. A key aspect of this study is the modeling of a fair-access criterion that requires sensors to have an equal rate of underwater frame delivery to the base station. Tight upper bounds on network utilization and tight lower bounds on the minimum time between samples are derived for fixed linear and grid topologies. The significance of these bounds is two-fold: First, they hold for any MAC protocol under both single-channel and half-duplex radios; second, they are provably tight. For underwater sensor networks, under certain conditions, we derive a tight upper bound on network utilization and demonstrate a significant fact that the utilization in networks with propagation delay is larger than that in networks with no propagation delay. The challenge of this work about underwater sensor networks lies in the fact that the propagation delay impact on underwater sensor networks is difficult to model. Finally, we explore bounds in networks with more complex topologies.