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We present photometric analysis of twelve Galactic open clusters and show that the same multiple-population phenomenon observed in Magellanic Clouds (MCs) is present in nearby open clusters. Nearly all the clusters younger than $\sim$2.5 Gyr of both MCs exhibit extended main-sequence turnoffs (eMSTOs) and all the cluster younger than $\sim$700 Myr show broadened/split main sequences (MSs). High-resolution spectroscopy has revealed that these clusters host stars with a large spread in the observed projected rotations. In addition to rotation, internal age variation is indicated as a possible responsible for the eMSTOs, making these systems the possible young counterparts of globular clusters with multiple populations. Recent work has shown that the eMSTO+broadened MSs are not a peculiarity of MCs clusters. Similar photometric features have been discovered in a few Galactic open clusters, challenging the idea that the color-magnitude diagrams (CMDs) of these systems are similar to single isochrones and opening new windows to explore the eMSTO phenomenon. We exploit photometry+proper motions from Gaia DR2 to investigate the CMDs of open clusters younger than $\sim$1.5 Gyr. Our analysis suggests that: (i) twelve open clusters show eMSTOs and/or broadened MSs, that cannot be due neither to field contamination, nor binaries; (ii) split/broadened MSs are observed in clusters younger than $\sim$700 Myr, while older objects display only an eMSTO, similarly to MCs clusters; (iii) the eMSTO, if interpreted as a pure age spread, increases with age, following the relation observed in MCs clusters and demonstrating that rotation is the responsible for this phenomenon.