  We present an extensive analysis of transport properties in superdiffusive
two dimensional quenched random media, obtained by packing disks with radii
distributed according to a L\'evy law. We consider transport and scaling
properties in samples packed with two different procedures, at fixed filling
fraction and at self-similar packing, and we clarify the role of the two
procedures in the superdiffusive effects. Using the behavior of the filling
fraction in finite size systems as the main geometrical parameter, we define an
effective L\'evy exponents that correctly estimate the finite size effects. The
effective L\'evy exponent rules the dynamical scaling of the main transport
properties and identify the region where superdiffusive effects can be
detected.
