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Massive black hole (MBH) binary inspiral time scales are uncertain, and theirspins are even more poorly constrained. Spin misalignment, along with unequalmass ratios and spin magnitudes, introduces asymmetry in the gravitationalradiation, which imparts a recoil kick to the merged MBH. Understanding how MBHbinary spins evolve is crucial for determining their recoil velocities, theirgravitational wave (GW) waveforms detectable with LISA, as well as theirpost-merger retention rate in galaxies and thus their subsequent merger rate.Here we present a novel study that introduces a sub-resolution model for gas-and GW-driven MBH binary spin evolution using a population of accreting MBHsfrom the Illustris cosmological hydrodynamics simulations. We also modelsub-resolution binary inspiral via dynamical friction, stellar scattering,viscous gas drag, and GW emission. Our model assumes differential accretion,which causes greater alignment of the secondary MBH spin in unequal-massmergers. We find that 47% of the MBHs in our population merge by $z=0$. Ofthese, 19% have misaligned primaries and 10% have misaligned secondaries at thetime of merger in our (conservative) fiducial model. The MBH misalignmentfraction depends strongly on the accretion disc parameters, however. Reducingaccretion rates by a factor of 100, in a thicker disc, yields 79% and 42%misalignment for primaries and secondaries, respectively. Even in the fiducialmodel, more than 12% of binaries experience recoils of $>500$ km s$^{-1}$,which could displace them at least temporarily from galactic nuclei. Weadditionally find that a significant number of systems experience strongprecession.

Massive black hole binary inspiral and spin evolution in a cosmological framework