Merger rate density of BHNSs as a function of the redshift, z. The colored lines show the distributions for all the simulated Pop. III models. The thick solid blue line represents our fiducial model for Pop. III stars (log1). The thick solid gray line is the fiducial model for Pop. II stars (kro1); the shaded gray area encompasses the uncertainties on galactic outflows and IMF parameters (see Sect. 2.7). Finally, the thick solid black line represents the MRD of Pop. II-I BHNSs estimated by Iorio et al. (2023).