We calculate the electronic width of quantum wires as a function of their lithographic width in analogy to experiments performed on nanostructures defined by local oxidation of Ga[Al]As heterostructures. Two--dimensional simulations of two parallel oxide lines on top of a Ga[Al]As heterostructure defining a quantum wire are carried out in the framework of Density Functional Theory in the Local Density Approximation and are found to be in agreement with measurements. Quantitative assessment of the influence of various experimental uncertainties is given. The most influential parameter turns out to be the oxide line depth, followed by its exact shape and the effect of background doping (in decreasing order).
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