Electrical current is measured during scanning probe oxidation by performing force versus distance curves under the application of a positive sample voltage. It is shown how the time dependence of the current provides information about the kinetics of oxide growth under conditions in which the tip-surface distance is known unequivocally during current acquisition. Currentmeasurements at finite tip-sample distance, in particular, unveil how the geometry of the meniscus influences its electrical conduction properties as well as the role of space charge at very small tip-sample distances.