  Due to the competition between spatial and magnetic confinement, the density
of states of a quasi two-dimensional system deviates from the ideal step-like
form both quantitatively and qualitatively. We study how this affects the
spin-subband populations and the spin-polarization as functions of the
temperature, $T$, and the in-plane magnetic field, $B$, for narrow to wide
dilute-magnetic-semiconductor quantum wells. We focus on the quantum well
width, the magnitude of the spin-spin exchange interaction, and the sheet
carrier concentration dependence. We look for ranges where the system is
completely spin-polarized. Increasing $T$, the carrier spin-splitting,
$U_{o\sigma}$, decreases, while increasing $B$, $U_{o\sigma}$ increases.
Moreover, due to the density of states modification, all energetically higher
subbands become gradually depopulated.
