equal to $m(t)$. The quantity $u_i(t)$ is called the *potential* of site $i$ at time $t$.

The growth process describes the following random sequential allocation procedure. Arriving particles are sequentially allocated at sites of $\M$ such that a particle is allocated uniformly over sites with minimal potential. Then the process component $\xi_k(t)$ is the number of particles at site $k$ at time $t$. The growth process can be viewed as a certain limit case of a growth process studied in [@ShchVolk]. The growth process in [@ShchVolk] is defined as a discrete-time Markov chain $(\xi_i(t),\, i\in\M,\, t\in {\mathbb{Z}}_{+}),$ with values in ${\mathbb{Z}}^{M}_{+}$ and specified by the following transition probabilities $$\label{growth}
\P\{\xi_i(t+1)=\xi_{i}(t)+1,\ \xi_j(t+1)=\xi_j(t)\ \forall j\ne
i\|\xi(t)\}= \frac{\beta^{u_i(t)}}{Z(\xi(t))}$$ where $$Z(\xi(t))=\sum_{j=1}^{M}\beta^{u_j(t)},$$ $\beta$ is a positive number and the other notations are the same as before. It is easy to see that the process defined by transition probabilities (\[tran\]) is the corresponding limit process as $\beta{\rightarrow}0$. In turn, the growth process specified by the transition probabilities (\[growth\]) is a particular version of the [cooperative sequential adsorption model (CSA)]{}. CSA is a probabilistic model which is widely used in physics for modelling various adsorption processes (see [@Evans], [@Privman] and references therein). Some asymptotic and statistical studies 