The motivation of the present work is to perform an analysis as comple
te as possible of the constraints that the dipole structure in the dis
tribution of galaxy clusters can put on dark-matter models, We use sim
ulations of the cluster distribution, based on the Zel'dovich approxim
ation, starting from different values of the fundamental cosmological
parameters, like Omega(0), Delta and the dark-matter components, The r
elative cheapness in CPU time of Zel'dovich approach allows us to run
many realizations for a large number of different models of the Univer
se. Our main results can be summarized as follows. Local Group like ob
servers are likely produced in Omega(0) = 1 models, quite irrespective
ly of the detailed power-spectrum shape, while they are more rare in t
he Omega(0) = 0.2 CDM models. Misalignment between the directions of t
he CMB and cluster dipoles like that observed occurs quite often, alth
ough an accurate alignment is not always guaranteed. About 30%, 40% of
the observers measure a misalignment below 20 degrees. The observed c
luster dipole amplitude is more typical in the four high-density (Omeg
a(0) = 1) models than in the low - density (Omega(0) = 0.2) ones. Inde
pendent estimates of the cluster biasing factor in the simulations all
ows to work out the value of Omega(0) from cluster dipoles. It turns o
ut that the input value (Omega(0) = 1 or 0.2) is recovered quite well,
thus supporting the reliability of cluster dipole to measure the aver
age matter density in the Universe.