In our previous work we investigated numerically the influence of the steric properties of conducting particles in a non-conducting host matrix on the electrical conductivity threshold of the material, especially in regard to the shape and orientational order of the particles. In the present work we consider theoretically some additional geometrical aspects of the percolation problem. As regards the percolation threshold itself, we consider three aspects: the probability of inter-penetration of half-soft conducting particles for different penetration depths (penetration probability function), different kinds of inhomogeneous distribution of particles in non-conducting host, size effects, and the agglomeration of conducting particles. We also analyze the size of the conducting-particles' clusters below and above the percolation threshold and compare some characteristic critical exponents with the results in the literature.