  The quantum Hall effect is a remarkable manifestation of quantized transport
in a two-dimensional electron gas. Given its technological relevance, it is
important to understand its development in realistic nanoscale devices. In this
work we present how the appearance of different edge channels in a field-effect
device is influenced by the inhomogeneous capacitance profile existing near the
sample edges, a condition of particular relevance for graphene. We apply this
practical idea to experiments on high quality graphene, demonstrating the
potential of quantum Hall transport as a spatially resolved probe of density
profiles near the edge of this two-dimensional electron gas.
