  We investigate the properties of the host galaxies of compact binary mergers
across cosmic time, by means of population-synthesis simulations combined with
galaxy catalogues from the EAGLE suite. We analyze the merger rate per galaxy
of binary neutron stars (BNSs), black hole--neutron star binaries (BHNSs) and
binary black holes (BBHs) from redshift zero up to redshift six. The binary
merger rate per galaxy strongly correlates with the stellar mass of the host
galaxy at any redshift considered here. This correlation is significantly
steeper for BNSs than for both BHNSs and BBHs. Moreover, we find that the
merger rate per galaxy depends also on host galaxy's star formation rate and
metallicity. We derive a robust fitting formula that relates the merger rate
per galaxy with galaxy's star formation rate, stellar mass and metallicity at
different redshifts. The typical masses of the host galaxies increase
significantly as redshift decreases, as a consequence of the interplay between
delay time distribution of compact binaries and cosmic assembly of galaxies.
Finally, we study the evolution of the merger rate density with redshift. At
low redshift ($z\leq{}0.1$) early-type galaxies give a larger contribution to
the merger rate density than late-type galaxies. This trend reverts at
$z\ge{}1$.
