  We present an in-depth analysis of the geometrical percolation behavior in
the continuum of random assemblies of hard oblate ellipsoids of revolution.
Simulations where carried out by considering a broad range of aspect-ratios,
from spheres up to aspect-ratio 100 plate-like objects, and with various
limiting two particle interaction distances, from 0.05 times the major axis up
to 4.0 times the major axis. We confirm the widely reported trend of a
consistent lowering of the hard particle critical volume fraction with the
increase of the aspect-ratio. Moreover, assimilating the limiting interaction
distance to a shell of constant thickness surrounding the ellipsoids, we
propose a simple relation based on the total excluded volume of these objects
which allows to estimate the critical concentration from a quantity which is
quasi-invariant over a large spectrum of limiting interaction distances.
Excluded volume and volume quantities are derived explicitly.
