Properties of MBH binaries and their host galaxies, for systems dominating the background and CW candidates. Top: Eddington ratio of the binary averaged over 1 Myr around the time when the MBHs merge. Bottom: SFR averaged over 100 Myr. The teal dotted histogram shows the MBHBs dominating the background, selected in the simulation box. The red-hatched histogram shows CW candidates, with the gray histogram highlighting the high probability ones. MBHs with f_Edd = 0 are shown at f_Edd = 10⁻⁸ and galaxies with SFR = 100 Myr = 0 are shown at SFR = 100 Myr = 10⁻³. In these distributions we include CW candidates accounting for their multiplicity across Universe realizations.