The hot intra-cluster medium (ICM) permeating galaxy clusters and groups is not pristine, as it has been continuously enriched by metals synthesised in Type Ia (SNIa) and core-collapse (SNcc) supernovae since the major epoch of star formation (z ≃ 2-3). The cluster/group enrichment history and mechanisms responsible for releasing and mixing the metals can be probed via the radial distribution of SNIa and SNcc products within the ICM. In this paper, we use deep XMM-Newton/EPIC observations from a sample of 44 nearby cool-core galaxy clusters, groups, and ellipticals (CHEERS) to constrain the average radial O, Mg, Si, S, Ar, Ca, Fe, and Ni abundance profiles. The radial distributions of all these elements, averaged over a large sample for the first time, represent the best constrained profiles available currently. Specific attention is devoted to a proper modelling of the EPIC spectral components, and to other systematic uncertainties that may affect our results. We find an overall decrease of the Fe abundance with radius out to 0.9 r500 and 0.6 r500 for clusters and groups, respectively, in good agreement with predictions from the most recent hydrodynamical simulations. The average radial profiles of all the other elements (X) are also centrally peaked and, when rescaled to their average central X/Fe ratios, follow well the Fe profile out to at least 0.5 r500. As predicted by recent simulations, we find that the relative contribution of SNIa (SNcc) to the total ICM enrichment is consistent with being uniform at all radii, both for clusters and groups using two sets of SNIa and SNcc yield models that reproduce the X/Fe abundance pattern in the core well. In addition to implying that the central metal peak is balanced between SNIa and SNcc, our results suggest that the enriching SNIa and SNcc products must share the same origin and that the delay between the bulk of the SNIa and SNcc explosions must be shorter than the timescale necessary to diffuse out the metals. Finally, we report an apparent abundance drop in the very core of 14 systems ( 32% of the sample). Possible origins of these drops are discussed.
