  Using wave kinetics, we estimate the emergence time-scale of gravitating
Bose-Einstein condensates/Bose stars in the kinetic regime for a general
multicomponent Schr\"{o}dinger-Poisson (SP) system. We identify some effects of
the diffusion and friction pieces in the wave-kinetic Boltzmann equation (at
leading order in perturbation theory) and provide estimates for the kinetic
nucleation rate of condensates. We test our analysis using full $3+1$
dimensional simulations of multicomponent SP system. With an eye towards
applications to multicomponent dark matter, we investigate two general cases in
detail. First is a massive spin-$s$ field with $N=2s+1$ components (scalar
$s=0$, vector $s=1$ and tensor $s=2$). We find that for a democratic population
of different components, the condensation time-scale is $\tau_{(s)}\approx
\tau_0\times N$, where $\tau_0$ is the condensation time scale for the scalar
case. Second is the case of two scalars with different boson masses. In this
case, we map-out how the condensation time depends on the ratios of their
average mass densities and boson masses, revealing competition and assistance
between components, and a guide towards which component condenses first. For
instance, with $m_1 < m_2$ and not too disparate mass densities, we verify that
the time scale of condensation of the first species quickly becomes independent
of $m_2/m_1$, whereas for equal average number densities, the emergence time
scale decreases with increasing $m_2/m_1$.
