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(Abridged) We have used Gaia EDR3 data, together with spectra of a largesample of luminous stars in the field surrounding Westerlund 1, to explore theextent of the cluster. We carry out a non-parametric analysis of proper motionsand membership determination. We investigate the reddening and proper motionsof several dozen OB stars and red supergiants < 1 deg away from Wd 1. Weidentify a population of kinematic members of Wd 1 that largely includes theknown spectroscopic members. From their EDR3 parallaxes, we derive a distanceto the cluster of $4.23^{+0.23}_{-0.21}$kpc. Extinction in this directionincreases by a large amount around 2.8 kpc, due to dark clouds associated tothe Scutum-Crux arm. As a consequence, we hardly see any stars at distancescomparable to that of the cluster. The proper motions of Wd 1, however, arevery similar to those of stars in the field surrounding it, but distinct. Wefind a second, astrometrically well-defined population in the foreground($d\approx2\:$kpc), likely connected to the possible open cluster BH197. Wd 1is very elongated, an effect not driven by the very heavy extinction to theEast and South. We find a low-density halo extending up to 10' from the clustercentre, mainly in the NW quadrant. A few OB stars at larger distances from thecluster, most notably the LBV MN48, share its proper motions, suggesting thatWd 1 has little or no peculiar motion with respect to the field population ofthe Norma arm. However, we are unable to find any red supergiant that couldbelong to an extended population related to the cluster, although we observeseveral dozen such objects in the foreground. We find a substantial populationof luminous OB members obscured by several more magnitudes of extinction thanmost known members. These objects, mostly located in the central region of thecluster, increase the population of OB supergiants by about 25%.

Westerlund 1 under the light of Gaia EDR3: Distance, isolation, extent, and a hidden population