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We formulate a rigorous nonlinear analytical model that describes the dynamics of the diffusion (reconnection) region in driven systems in the context of electron magnetohydrodynamics (EMHD). A steady-state analysis yields allowed geometric configurations and associated reconnection rates. In addition to the well-known open X-point geometry, elongated configurations are found possible. The model predictions have been validated numerically with two-dimensional EMHD nonlinear simulations, and are in excellent agreement with previously published work.