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Understanding the influence of dark energy on the formation of structures iscurrently a major challenge in Cosmology, since it can distinguish otherwisedegenerated viable models. In this work we consider the Top-HatSpherical-Collapse (SC) model with dark energy, which can partially (ortotally) cluster, according to a free parameter $\gamma$. The {\it lack of}energy conservation has to be taken into account accordingly, as we will show.We determine characteristic quantities for the SC model, such as the criticalcontrast density and radius evolution, with particular emphasis on theirdependence on the clustering parameter $\gamma$.

Top-Hat Spherical Collapse with Clustering Dark Energy. I. Radius Evolution and Critical Contrast Density