Context. The spectral classifications of the Galactic O-Star Spectroscopic Survey (GOSSS) and the astrometric and photometric data from Gaia have significantly improved our ability to measure distances and determine memberships of stellar groups (clusters, associations, or parts thereof) with OB stars. In the near future, the situation will be further improved thanks to subsequent Gaia data releases and new photometric and spectroscopic surveys. Aims. We initiated a program to identify and determine the membership of Galactic stellar groups with OB stars and measure distances to them. Given the data currently available, we started with the identification and distance determinations of groups with O stars. In this paper, we concentrate on groups that contain stars with the earliest spectral subtypes. Methods. We used GOSSS to select Galactic stellar groups with O2–O3.5 stars and the method described in paper 0 of this series, which combines Gaia DR2 G + GBP + GRP photometry, positions, proper motions, and parallaxes to assign robust memberships and measure distances. We also included Collinder 419 and NGC 2264, the clusters cited in that paper, to generate our first list of 16 O-type Galactic stellar groups. Results. We derived distances, determined the membership, and analyzed the structure of sixteen Galactic stellar groups with O stars, Villafranca O-001 to Villafranca O-016, including the fourteen groups with the earliest-O-type optically accessible stars known in the Milky Way. We compared our distance with previous results from the literature and establish that the best consistency is with (the small number of) VLBI parallaxes and the worst is with kinematic distances. Our results indicate that very massive stars can form in relatively low-mass clusters or even in near-isolation, as is the case for the Bajamar star in the North America nebula. This lends support to the hierarchical scenario of star formation, where some stars are born in well-defined bound clusters but others are born in associations that are unbound from the beginning: groups of newborn stars come in many shapes and sizes. We propose that HD 64 568 and HD 64 315 AB could have been ejected simultaneously from Haffner 18 (Villafranca O-012 S). Our results are consistent with a difference of ≈20 μas in the Gaia DR2 parallax zero point between bright and faint stars.

Context. This is the second paper of a series on Galactic OB groups that uses astrometric and photometric data from Gaia and spectral classifications from the Galactic O-Star Spectroscopic Survey (GOSSS) and the Library of Libraries of Massive-star high-Resolution spectra (LiLiMaRlin). The previous paper was based on the second Gaia data release (DR2). Since then, the early third Gaia data release (EDR3) has appeared with new astrometry and photometry. Aims. The two aims of this paper are to revise the results for the sample from paper I using Gaia EDR3 data and to expand the sample of analyzed stellar groups to 26, from Villafranca O-001 to Villafranca O-026. Methods. We used GOSSS to select Galactic stellar groups with O stars and an updated version of the method in paper 0 of this series, combining Gaia EDR3 G + G BP + G RP photometry, positions, proper motions, and parallaxes to assign memberships and measure distances. We present 99 spectra from GOSSS and 32 from LiLiMaRlin for stars in the analyzed groups or in their foreground.Results. We derived distances to the 26 stellar groups with unprecedented precision and accuracy, with total (random plus systematic) uncertainties lower than 1% for distances within 1 kpc and of ∼3% around 3 kpc, which are values almost four times better than for Gaia DR2. We provide homogeneous spectral types for 110 stars and correct a number of errors in the literature, especially for objects in Villafranca O-023 (Orion nebula cluster). For each group, we discuss its membership and present possible runaway and walkaway stars. At least two of the studied groups, Villafranca O-O12 S in NGC 2467 and Villafranca O-014 NW in the North America nebula, are orphan clusters in which the most massive stars have been ejected by dynamical interactions, leaving objects with a capped mass function. The existence of such clusters has important consequences for the study of the initial mass function (IMF), the distribution of supernova explosions across the Galaxy, and the population and dynamics of isolated compact objects. We fit pre-main-sequence (PMS) isochrones to the color-magnitude diagrams (CMDs) of four clusters to derive ages of 2.0±0.5 Ma for Villafranca O-026 (σ Orionis cluster), 4±2 Ma for Villafranca O-016 (NGC 2264), 5.0±0.5 Ma for Villafranca O-021 (NGC 2362), and 8±2 Ma for Villafranca O-024 (γ Velorum cluster).