Context. We present the analysis of the galaxy structural parameters from Hα3, an Hα narrow-band imaging follow-up survey of ∼800 galaxies selected from the HI Arecibo Legacy Fast ALFA Survey (ALFALFA) in the Local supercluster, including the Virgo cluster, and in the Coma supercluster. Aims. Taking advantage of Hα3, which provides the complete census of the recent star-forming, HI-rich galaxies in the local universe, we aim to investigate the structural parameters of the young (<10 Myr) and the old (>1 Gyr) stellar populations. By comparing the sizes of these stellar components, we investigated the spatial scale on which galaxies are growing at the present cosmological epoch and the role of the environment in quenching the star-formation activity. Methods. We computed the concentration, asymmetry, and clumpiness (CAS) structural parameters for recently born and old stars. To quantify the sizes we computed half-light radii and a new parameter dubbed EW/r based on the half-light radius of the Hα equivalent width map. To highlight the environmental perturbation, we adopt an updated calibration of the HI-deficiency parameter (De f HI ) that we use to divide the sample in unperturbed galaxies (De f HI ≤ 0.3) and perturbed galaxies (De f HI > 0.3). Results. The concentration index computed in the r band depends on the stellar mass and on the Hubble type these variables are related because most massive galaxies are bulge dominated therefore highly concentrated. Going toward later spirals and irregulars the concentration index and the mass decrease along with the bulge-to-disk ratio. Blue compact dwarfs (BCDs) are an exception because they have similar mass, but they are more concentrated than dwarf irregulars. The asymmetry and the clumpiness increase along the spiral sequence up to Sc-Sd, but they decrease going in the dwarf regime, where the light distribution is smooth and more symmetric. When measured on Hα images, the CAS parameters show no obvious correlations with Hubble type. Irrespective of whether we used the ratio between effective radii or the EW/r parameter, we found that the concentration index is the main parameter that describes the current growth of isolated galaxies but, for a fixed concentration, the stellar mass plays a second-order role. At the present epoch, massive galaxies are growing inside-out, conversely, the dwarfs are growing on the scale of their already assembled mass.