  We calculate the nonequilibrium differential conductance $G(V)$ through a
quantum dot as function of bias voltage $V$ and applied magnetic field $H$. We
use a Keldysh conserving approximation for weakly correlated and the scattering
states numerical renormalization group for the intermediate and strongly
correlated regime out of equilibrium. In the weakly correlated regime, the
Zeeman splitting observable in $G(V)$ strongly depends on the asymmetry of the
coupling to the two leads, as well as on particle-hole asymmetry of the quantum
dot. In contrast, in the strongly correlated regime, where Kondo-correlations
dominate, the position $\Delta_K$ of the Zeeman-split zero-bias anomaly is
independent of such asymmetries and always found to be of the order of the
Zeeman energy $\Delta_0$. We find a crossover from the purely spin-fluctuation
driven Kondo regime at small magnetic fields with $\Delta_K<\Delta_0$ to a
regime at large fields where the contribution of charge fluctuations induces
larger splittings with $\Delta_K>\Delta_0$ as it was observed in recent
experiments.
