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The finite-element method is used to solve Poisson's equation, under equilibrium conditions, for coaxial carbon nanotube field-effect transistors in which the gate electrode does not entirely cover the nanotube channel between the source- and drain-end contacts. A conformal transformation is applied to overcome the problems that arise in this open structure of specifying boundary conditions and of terminating the model space. The effect on the potential distribution within the transistor of changing various geometrical properties of the device is investigated, and some special conditions under which appropriate boundary conditions may be defined a priori are identified. The effects on the potential energy profile along the nanotube of varying the work function of the end contacts, and of introducing charge into the gate dielectric, are also investigated. The latter is shown to be effective in suppressing the otherwise dominant role that the end contacts play in determining the barrier to charge flow in the nanotube, thereby allowing bulk control to occur.