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The electrostatics of nanowire transistors are studied by solving the Poisson equation self-consistently with the equilibrium carrier statistics of the nanowire. For a one-dimensional, intrinsic nanowire channel, charge transfer from the metal contacts is important. We examine how the charge transfer depends on the insulator and the metal/semiconductor Schottky barrier height. We also show that charge density on the nanowire is a sensitive function of the contact geometry. For a nanowire transistor with large gate underlaps, charge transferred from bulk electrodes can effectively "dope" the intrinsic, ungated region and allow the transistor to operate. Reducing the gate oxide thickness and the source/drain contact size decreases the length by which the source/drain electric field penetrates into the channel, thereby, improving the transistor characteristics.