  We study numerically the crossover between organized and disorganized states
of three non-equilibrium systems: the Poisson/coalesce random walk (PCRW), a
one-dimensional spin system and a quasi one-dimensional lattice gas. In all
cases, we describe this crossover in terms of the average spacing between
particles/domain borders $< S(t) >$ and the spacing distribution functions
$p^{(n)}(s)$. The nature of the crossover is not the same for all systems,
however, we found that for all systems the nearest neighbor distribution
$p^{(0)}(s)$ is well fitted by the Berry-Robnik model. The destruction of the
level repulsion in the crossover between organized an disorganized states is
present in all systems. Additionally, we found that the correlations between
domains in the gas and spin systems are not strong and can be neglected in a
first approximation but for the PCRW the correlations between particles must be
taken into account. To find $p^{(n)}(s)$ with $n>1$, we propose two different
analytical models based on the Berry-Robnik model. Our models give us a good
approximation for the statistical behavior of these systems in their crossover
and allow us to quantify the degree of order/disorder of the system.
