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This paper tackles the issue of downscaling of an ohmic contact from the infinite approximation to nanometer dimensions. Using the finite-element simulation program, it is shown that small-size ohmic contacts on a wide-bandgap semiconductor exhibit nonlinear current-voltage dependence in case velocity saturation is introduced. Furthermore, the dependence becomes asymmetrical around zero bias. In addition, it is shown that in small-size contacts, a nonlocal tunneling is bound to occur even in pure ohmic contacts. This may explain the absence of linear I-V curves in the reported experiments with nanometer-scale contacts.