  The dynamical state and morphological features of galaxies and galaxy
clusters, and their high-redshift precursors, are tightly connected with their
assembly history, encoding crucial information about the formation and
evolution of such cosmic structures. As a first step towards finding an optimal
indicator of the assembly state of observed structures, we use a cosmological
simulation of a moderate volume to critically examine the best definition of an
indicator that is able to discriminate dark matter haloes undergoing mergers
and/or strong accretion from haloes experimenting a relaxed evolution. Using a
combination of centre offset, virial ratio, mean radial velocity, sparsity and
ellipticity of the dark matter halo, we study how the thresholds on these
parameters, as well as their relative weights, should evolve with redshift to
provide the best classification possible. This allows us to split a sample of
haloes in a totally relaxed, a marginally relaxed and an unrelaxed subsamples.
The resulting classification strongly correlates with the merging activity
obtained from the analysis of complete merger trees extracted from whole
simulation data. The results on how the different indicators depend on redshift
and halo mass, and their optimal combination to better match the true assembly
history of haloes, could constitute relevant hints to find a suitable set of
indicators applicable to observational data.
