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In this paper, we present a novel view on the morphology and the dynamical state of 10 prominent, nearby ($\leq$ 500 pc), and young ($\sim$30-300 Myr) open star clusters with Gaia DR2: $α\,$Per, Blanco 1, IC 2602, IC 2391, Messier 39, NGC 2451A, NGC 2516, NGC 2547, Platais 9, and the Pleiades. We introduce a pioneering member identification method that is informed by cluster bulk velocities and deconvolves the spatial distribution with a mixture of Gaussians. Our approach enables inferring the clusters' true spatial distribution by effectively filtering field star contaminants while at the same time mitigating the impact of positional errors along the line of sight. This first application of the method reveals the existence of vast stellar coronae, extending for $\gtrsim\,$100 pc and surrounding the, by comparison tiny and compact, cluster cores. The coronae and cores form intertwined, co-eval, and co-moving extended cluster populations, each encompassing tens of thousands of cubic parsec and stretching across tens of degrees on the sky. Our analysis shows that the coronae are gravitationally unbound but largely comprise the bulk of the populations' stellar mass. Most systems are in a highly dynamic state, showing evidence of expansion and sometimes simultaneous contraction along different spatial axes. The velocity field of the extended populations for the cluster cores appears asymmetric but is aligned along a spatial axis unique to each cluster. The overall spatial distribution and the kinematic signature of the populations are largely consistent with the differential rotation pattern of the Milky Way. This finding underlines the important role of global Galactic dynamics to the fate of stellar systems. Our results highlight the complexity of the Milky Way's open cluster population and call for a new perspective on the characterization and dynamical state of open clusters.