  We investigate the transport properties of a complex porous structure with
branched fractal architectures formed due to the gradual deposition of dimers
in a model of multilayer adsorption. We thoroughly study the interplay between
the orientational anisotropy parameter $p_0$ of deposited dimers and the
formation of porous structures, as well as its impact on the conductivity of
the system, through extensive numerical simulations. By systematically varying
the value of $p_0$, several critical and off-critical scaling relations
characterizing the behavior of the system are examined. The results demonstrate
that the degree of orientational anisotropy of dimers plays a significant role
in determining the structural and physical characteristics of the system. We
find that the Einstein relation relating to the size scaling of the electrical
conductance holds true only in the limiting case of $p_0 \to 1$. Monitoring the
fractal dimension of the interface of the multilayer formation for various
$p_0$ values, we reveal that in a wide range of $p_0 > 0.2$ interface shows the
characteristic of a self-avoiding random walk, compared to the limiting case of
$p_0 \to 0$ where it is characterized by the fractal dimension of the backbone
of ordinary percolation cluster at criticality. Our results thus can provide
useful information about the fundamental mechanisms underlying the formation
and behavior of wide varieties of amorphous and disordered systems that are of
paramount importance both in science and technology as well as in environmental
studies.
