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(Abridged) The lifetime of protoplanetary disks around young stars limits the timescale when planets form. A disk dissipation timescale < 10 Myr was inferred from surveys providing the fraction of stars with disks in young stellar clusters with different ages. However, most previous surveys focused on the compact region within ~ 2 pc from the clusters' centers, for which the disk fraction information considering the outer part is practically absent. We aim to test if disk fraction estimates change when inferred from an extended region around the clusters' centers. Gaia EDR3 data and a best-suited, Virtual Observatory (VO)-based tool -Clusterix-, are used to identify member stars for a representative sample of 19 young clusters considering two concentric fields of view (FOV) with radii ~ 20 pc and ~ 2 pc. Our analysis reveals that the inner disk fractions inferred from the compact and the extended regions are equal within ~ 10%, which does not support a previous hypothesis proposing that disk fractions should be significantly larger considering extended regions. A list of member and disk stars in each cluster is provided and stored in a VO-compliant archive. Averaged values and plots characterizing the whole clusters are also provided, including HR diagrams based on Gaia colors and absolute magnitudes. Our results cover the largest fields ever probed when dealing with disk fractions for all clusters analysed, and imply that their complete characterization requires the use of wide FOVs. The resulting database is a benchmark for future detailed studies of young clusters, whose disk fractions must be accurately determined by using multi-wavelength analysis potentially combined with data from coming Gaia releases.