  Supermassive black-hole binaries are driven to merger by dynamical friction,
loss-cone scattering of individual stars, disk migration, and
gravitational-wave emission. Two main formation scenarios are expected.
Binaries that form in gas-poor galactic environments do not experience disk
migration and likely enter the gravitational-wave dominated phase with roughly
isotropic spin orientations. Comparatively, binaries that evolve in gas-rich
galactic environments might experience prominent phases of disk accretion,
where the Bardeen-Petterson effect acts to align the spins of the black holes
with the orbital angular momentum of the disk. However, if the accretion disk
breaks alignment is expected to be strongly suppressed -- a phenomenon that was
recently shown to occur in a large portion of the parameter space. In this
paper, we develop a semi-analytic model of joint gas-driven migration and spin
alignment of supermassive black-hole binaries taking into account the impact of
disk breaking for the first time. Our model predicts the occurrence of distinct
subpopulations of binaries depending on the efficiency of spin alignment. This
implies that future gravitational-wave observations of merging black holes
could potentially be used to (i) discriminate between gas-rich and gas-poor
hosts and (ii) constrain the dynamics of warped accretion disks.
