Rectangular Galactocentric (X, Y, Z) distribution of RCB (red dots), dLHdC (yellow dots), DYPer type (purple dots), and EHe stars (blue triangles) with a valid astrometric fit and a parallax S/N higher than 3. From top to bottom: X versus Y, Z versus X and Z versus the Galactic radius. On the left side, large-scale views presenting stars located in the Galactic halo. On the right side, closer-in views. We have indicated with grey lines the possible distances for some HdC stars that do not have significant parallaxes measured by Gaia DR3. We used a V absolute magnitude range between −5 and −3.5 mag (resp. −4.5 and −3 mag) for the warm (resp. cold) HdC stars, i.e. the HdC stars with a temperature classification lower or equal to HdC4 (resp. higher than HdC4). The location of the far away dLHdC star, HE 1015-2050, is indicated with an arrow and the coordinates of the two distances extremities in square brackets.