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Massive black hole (MBH) coalescences are powerful sources of low-frequency gravitational waves. To study these events in the cosmological context, we need to trace the large-scale structure and cosmic evolution of a statistical population of galaxies, from dim dwarfs to bright galaxies. To cover such a large range of galaxy masses, we analyse two complementary simulations: horizon-AGN with a large volume and low resolution that tracks the high-mass (⁠|$\gt 10^7\, {\rm M_\odot }$|⁠) MBH population, and NewHorizon with a smaller volume but higher resolution that traces the low-mass (|$\lt 10^7\, {\rm M_\odot }$|⁠) MBH population. While Horizon-AGN can be used to estimate the rate of inspirals for pulsar timing arrays, NewHorizon  can investigate MBH mergers in a statistical sample of dwarf galaxies for LISA, which is sensitive to low-mass MBHs. We use the same method to analyse the two simulations, post-processing MBH dynamics to account for time delays mostly determined by dynamical friction and stellar hardening. In both simulations, MBHs typically merge long after galaxies do, so that the galaxy morphology at the time of the MBH merger is no longer determined by the structural disturbances engendered by the galaxy merger from which the MBH coalescence has originated. These time delays cause a loss of high- z MBH coalescences, shifting the peak of the MBH merger rate to z ∼ 1–2. This study shows how tracking MBH mergers in low-mass galaxies is crucial to probing the MBH merger rate for LISA and investigate the properties of the host galaxies. [ABSTRACT FROM AUTHOR]