  Irreversible adsorption of objects of different shapes and sizes on
Euclidean, fractal and random lattices is studied. The adsorption process is
modeled by using random sequential adsorption (RSA) algorithm. Objects are
adsorbed on one-, two-, and three-dimensional Euclidean lattices, on Sierpinski
carpets having dimension $d$ between 1 and 2, and on Erdos-Renyi random graphs.
The number of sites is $M=L^d$ for Euclidean and fractal lattices, where $L$ is
a characteristic length of the system. In the case of random graphs it does not
exist such characteristic length, and the substrate can be characterized by a
fixed set of $M$ vertices (sites) and an average connectivity (or degree) $g$.
The paper concentrates on measuring (1) the probability $W_{L(M)}(\theta)$ that
a lattice composed of $L^d(M)$ elements reaches a coverage $\theta$, and (2)
the exponent $\nu_j$ characterizing the so-called "jamming transition". The
results obtained for Euclidean, fractal and random lattices indicate that the
main quantities derived from the jamming probability $W_{L(M)}(\theta)$ behave
asymptotically as $M^{1/2}$. In the case of Euclidean and fractal lattices,
where $L$ and $d$ can be defined, the asymptotic behavior can be written as
$M^{1/2} = L^{d/2}=L^{1/\nu_j}$, and $\nu_j=2/d$.

Statistical Mechanics