  It is well established that active-sterile neutrino oscillations generate
large neutrino asymmetries for very small mixing angles ($\sin^2
2\theta_0\lesssim 10^{-4}$), negative values of $\delta m^2$ and provided that
$|\delta m^2|\gtrsim 10^{-4} {\rm eV^2}$. By numerically solving the quantum
kinetic equations, we show that the generation still occurs at much lower
values of $|\delta m^2|$. We also describe the borders of the generation at
small mixing angles and show how our numerical results can be analytically
understood within the framework of the Landau-Zener approximation thereby
extending previous work based on the adiabatic limit. This approximate approach
leads to a fair description of the MSW dominated regime of the neutrino
asymmetry evolution and is also able to correctly reproduce its final value. We
also briefly discuss the impact that neutrino asymmetry generation could have
on big bang nucleosynthesis, CMBR and relic neutrinos.
