  We analytically solve the problem of Bose star growth in the bath of
gravitationally interacting particles. We find that after nucleation of this
object the bath is described by a self-similar solution of kinetic equation.
Together with the conservation laws, this fixes mass evolution of the Bose
star. Our theory explains, in particular, the slowdown of the star growth at a
certain "core-halo" mass, but also predicts formation of heavier and lighter
objects in magistral dark matter models. The developed "adiabatic" approach to
self-similarity may be of interest for kinetic theory in general.
