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Aims. With the goal of providing constraints on the nature of the progenitors of core-collapse (CC) supernovae (SNe), we compare their radial distribution within their spiral host galaxies with the distributions of stars and ionized gas in spiral disks. Methods. SNe positions are taken from the Asiago catalog for a well-defined sample of 224 SNe within 204 host galaxies. The SN radial distances are estimated from the deprojected separations from the host galaxy nuclei, and normalized both to the 25th ${\rm mag~arcsec}^{-2}$ blue-band isophotal radius and (for the first time) to the statistically-estimated disk scale length. Results. The normalized radial distribution of all CCSNe is consistent with an exponential law, as previously found, with a possible depletion of CCSNe within one-fifth of the isophotal radius (less significant with scale-length normalization). There are no signs of truncation of the exponential distribution of CCSNe out to 7 disk scale lengths. The scale length of the distribution of type II SNe appears to be significantly larger than that of the stellar disks of their host galaxies, but consistent with the scale lengths of Freeman disks. SNe Ib/c have a significantly smaller scale length than SNe II, with little difference between types Ib and Ic. The radial distribution of type Ib/c SNe is more centrally concentrated than that of the stars in a Freeman disk, but is similar to the stellar disk distribution that we infer for the host galaxies. All CCSN subsamples are consistent with the still uncertain distribution of $\ion{H}{ii}$ regions. The scale length of the CCSN radial distribution shows no significant correlation with the host galaxy morphological type, or the presence of bars. However, low luminosity as well as inclined hosts have a less concentrated distribution (with the scale-length normalized radial distances) of CCSNe, which are probably a consequence of metallicity and selection effects, respectively. Conclusions. The exponential distribution of CCSNe shows a scale length consistent with that of the ionized gas confirming the generally accepted hypothesis that the progenitors of these SNe are young massive stars. Given the lack of correlation of the normalized radial distances of CCSNe with the morphological type of the host galaxy, we conclude that the more concentrated distribution of SNe Ib/c relative to SNe II must arise from the higher metallicity of their progenitors or possibly from a shallower initial mass function in the inner regions of spirals.