I model the ocean as an array of lines set within a two-dimensional frame, and show how the Exclusive Economic Zone emerged as an equilibrium in customary international law. I find that custom codifies the efficient Nash equilibrium of enclosure for nearshore fisheries. For highly migratory and offshore fisheries, enclosure is inefficient, and customary law supports a more efficient "free sea" regime. The model also identifies the trigger for changes in property rights and the reason choice of a particular limit, like the current 200-mile zone, is arbitrary. In an asymmetric, regional sea, I find that the scope of the EEZ is determined by the relative power of coastal and distant water states, and need not be efficient. Finally, I find that proposals to nationalize the seas or ban fishing on the high seas are neither efficient nor supportable as equilibria in customary law.