  We have obtained the universal conductance distribution of two-dimensional
disordered systems in the strongly localized limit. This distribution is
directly related to the Tracy-Widom distribution, which has recently appeared
in many different problems. We first map a forward scattering paths model into
a problem of directed random polymers previously solved. We show numerically
that the same distribution also applies to other forward scattering paths
models and to the Anderson model. We show that most of the electric current
follows a preferential percolation-type path. The particular form of the
distribution depends on the type of leads used to measure the conductance. The
application of a moderate magnetic field changes the average conductance and
the size of uctuations, but not the distribution when properly scaled. Although
the presence of magnetic field changes the universality class, we show that the
conductance distribution in the strongly localized limit is the same for both
classes.
