We present the Morphology-Density and Morphology-Radius relations (T-Sigma and T-R, respectively) obtained from the WINGS database of galaxies in nearby clusters. Aiming to achieve the best statistics, we exploit the whole sample of galaxies brighter than MV=-19.5 (5,504 objects), stacking up the 76 clusters of the WINGS survey altogether. Using this global cluster sample, we find that the T-Sigma relation holds only in the inner cluster regions (R<1/3xR200), while the T-R relation keeps almost unchanged over the whole range of local density. A couple of tests and two sets of numerical simulations support the robustness of these results against the effects of the limited cluster area coverage of the WINGS imaging. The above mentioned results hold for all cluster masses (X-ray luminosity and velocity dispersion) and all galaxy stellar masses (M). The strength of the T-Sigma relation (where present) increases with increasing M, while this effect is not found for the T-R relation. Noticeably, the absence/presence of subclustering determines the presence/absence of the T-Sigma relation outside the inner cluster regions, leading us to the general conclusion that the link between morphology and local density is preserved just in dynamically evolved regions. We hypothesize that some mechanism of morphological broadening/redistribution operates in the intermediate/outer regions of substructured (non relaxed) clusters, producing a strong weakening of the T-Sigma relation.
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