  In the simple case of a constant equation of state, redshift distribution of
collapsed structures may constrain dark energy models. Different dark energy
models having the same energy density today but different equations of state
give quite different number counts. Moreover, we show that introducing the
possibility that dark energy collapses with dark matter (``inhomogeneous'' dark
energy) significantly complicates the picture. We illustrate our results by
comparing four dark energy models to the standard $\Lambda$-model. We
investigate a model with a constant equation of state equal to -0.8, a phantom
energy model and two scalar potentials (built out of a combination of two
exponential terms). Although their equations of state at present are almost
indistinguishable from a $\Lambda$-model, both scalar potentials undergo quite
different evolutions at higher redshifts and give different number counts. We
show that phantom dark energy induces opposite departures from the
$\Lambda$-model as compared with the other models considered here. Finally, we
find that inhomogeneous dark energy enhances departures from the
$\Lambda$-model with maximum deviations of about 15% for both number counts and
integrated number counts. Larger departures from the $\Lambda$-model are
obtained for massive structures which are rare objects making it difficult to
statistically distinguish between models.
