  Scalar fields around compact objects are of interest for scalar-tensor
theories of gravity and dark matter models consisting of a massive scalar, e.g.
axions. We study the behaviour of a scalar field around a Kerr black hole with
non trivial asymptotic boundary conditions - both non zero density and non zero
angular momentum. Starting from an initial radially homogeneous configuration,
a scalar cloud is accreted, which asymptotes to known stationary configurations
over time. We study the cloud growth for different parameters including black
hole spin, scalar field mass, and the scalar field density and angular momentum
far from the black hole. We characterise the transient growth of the mass and
angular momentum in the cloud, and the spatial profile of the scalar around the
black hole, and relate the results of fully non-linear simulations to an
analytic perturbative expansion. We also highlight the potential for these
accreted clouds to create monochromatic gravitational wave signals - similar to
the signals from superradiant clouds, although significantly weaker in
amplitude.
