  A random lattice model with dilute interlayer bonds of density $p$ is
proposed to describe the underdoped high--$T_c$ cuprates. We show analytically
via an appropriate perturbation expansion and verify independently by numerical
scaling of the conductance that for any finite $p$ the states remain extended
in all directions, despite the presence of interlayer disorder. However, the
obtained electronic transport is highly anisotropic with violent conductance
fluctuations occuring in the layering direction, which can be responsible for
the experimentally observed metallic "in-plane" and semiconducting
"out-of-plane" resistivity of the cuprates.
