  This paper is devoted to a direct martingale approach for P{\'o}lya urn
models asymptotic behaviour. A P{\'o}lya process is said to be small when the
ratio of its remplacement matrix eigenvalues is less than or equal to 1/2,
otherwise it is called large. We find again some well-known results on the
asymptotic behaviour for small and large urns processes. We also provide new
almost sure properties for small urns processes.
