  In this work, we calculate the electron and the current density distributions
both at the edges and the bulk of a two dimensional electron system, focusing
on ideal and non-ideal contacts. A three dimensional Poisson equation is solved
self-consistently to obtain the potential profile in the absence of an external
magnetic field considering a Hall bar defined both by gates (contacts) and
etching (lateral confinement). In the presence of a perpendicular magnetic
field, we obtain the spatial distribution of the incompressible strips, taking
into account the electron-electron interactions within the Thomas-Fermi
approximation. Using a local version of Ohm's law, together with a relevant
conductivity model, we also calculate the current distribution. We observe that
the incompressible strips can reside either on the edge or at the bulk
depending on the field strength. Our numerical results show that, due to a
density poor region just in front of the contacts, the incompressible strips do
not penetrate to the injection region when considering non-ideal contact
configuration. Such a non-ideal contact is in strong contrast with the
conventional edge channel pictures, hence has a strong influence on transport.
We also take into account heating effects in a phenomenological manner and
propose a current injection mechanism from the compressible regions to the
incompressible regions. The model presented here perfectly agrees with the
local probe experiments all together with the formation of hot-spots.
