In this paper we make an attempt to portray the current situation in the probabilistic combinatorics field where so-called generalised allocation scheme has been utilised. We offer a series of limit theorems for sums of independent identically distributed non-negative integer-valued random variables which are applicable when using generalised allocation schemes. We look at the phenomenon of the transition of the distribution of sums of independent identically distributed integer-valued random variables from one lattice to another in the context of the generalised allocation scheme, and give several examples on how to reduce a combinatorial problem to some kind of a generalised scheme of allocating particles to cells.