  The Chern-Simons Ginzburg-Landau theory for the fractional Quantum Hall
effect is studied in the presence of a confining potential. We review the bulk
properties of the model and discuss how the plateau formation emerges without
any impurity potential. The effect is related to changes, by accumulation of
charge, at the edge when the chemical potential is changed. Fluctuations about
the ground state are examined and an expression is found for the velocity of
the massless edge mode in terms of the confining potential. The effect of
including spin is examined for the case when the system is fully polarized in
the bulk. In general a spin texture may appear at the edge, and we examine this
effect in the case of a small spin down component. The low frequency edge modes
are examined and a third order equation is found for velocities which indicates
the presence of three different modes. The discussions are illustrated by
numerical studies of the ground states, both for the one- and two-component
cases.
