Canis Major OB1 (CMa OB1) is a Galactic stellar association with a very intriguing star-formation scenario. There are more than two dozen known star clusters in its line of sight, but it is not clear which ones are physically associated with CMa OB1. We use a clustering code that employs 5-dimensional data from the Gaia DR2 catalogue to identify physical groups and obtain their astrometric parameters and, in addition, we use two different isochrone-fitting methods to estimate the ages of these groups. We find 15 stellar groups with distances between 570 pc and 1650 pc, including 10 previously known and 5 new open cluster candidates. Four groups, precisely the youngest ones ($<$ 20 Myr), CMa05, CMa06, CMa07 and CMa08, are confirmed to be part of CMa OB1. We find that CMa08, a new cluster candidate, may be the progenitor cluster of runaway stars. CMa06 coincides with the well-studied CMa R1 star-forming region. While CMa06 is still forming stars, due to the remaining material of the molecular cloud associated with the Sh 2-262 nebula, CMa05, CMa07 and CMa08 seem to be in more evolved stages of evolution, with no recent star-forming activity. The properties of these CMa OB1 physical groups fit well in a monolithic scenario of star formation, with a common formation mechanism, and having suffered multiple episodes of star formation. This suggests that the hierarchical model alone, which explains the populations of other parts of the same association, is not sufficient to explain its whole formation history.
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