  We consider the role of the third dimension in the conductivity of a quasi 2D
electron gas. If the transverse correlation radius of the scattering potential
is smaller than the width of the channel, i.e. the width of the transverse
electron density distribution, then scattering to higher levels of the
confinement potential becomes important, which causes a broadening of the
current flow profile. The resulting conductivity is larger than that obtained
from a 2D Boltzmann equation. A magnetic field, parallel to the driving
electric field, effectively competes with the confining potential and, in the
limit of a strong magnetic field, it is the field, which largely shapes the
electron and current profile, rather than the potential. As a result the
current flow profile increases and a negative longitudinal magnetoresistivity
of the quasi 2D electron gas may be observed.
