The steady‐state behavior of the magnetized plasma–wall sheath has been studied through two‐dimensional particle simulations, which have shown that the sheath maintains itself in a strongly nonlinear, turbulent equilibrium, continuously driven by the edge Kelvin–Helmholtz instability. The sheath assumes a thickness of orderlx∼5&rgr;i, and maintains large, long‐lived vortices, with amplitudes &dgr;&fgr;∼2.5Ti/e, which drift parallel to the wall at half the ion thermal velocity. The sheath also maintains a large, spatially averaged potential drop from the wall to the plasma with &Dgr;&fgr;≊−2Ti/e, opposite in sign to that of the unmagnetized sheath. Accompanying the long‐wavelength vortices are shorter‐wavelength fluctuations, which induce an anomalous cross‐field transport, scaling in accordance to Bohm diffusion when &ohgr;pi≥2&ohgr;ci. At lower densities, &ohgr;pi<2&ohgr;ci, the diffusion coefficient has an additional factor, proportional to the density. These results permit the modeling of the cross‐field sheath by a simple effective boundary condition.