  We study the effects of spin-flip scatterings on the time-dependent transport
properties through a magnetic quantum dot attached to normal and ferromagnetic
leads. The transient spin-dynamics as well as the steady-state tunneling
magnetoresistance (TMR) of the system are investigated. The absence of a
definite spin quantization axis requires the time-propagation of two-component
spinors. We present numerical results in which the electrodes are treated both
as one-dimensional tight-binding wires and in the wide-band limit
approximation. In the latter case we derive a transparent analytic formula for
the spin-resolved current, and transient oscillations damped over different
time-scales are identified. We also find a novel regime for the TMR inversion.
For any given strength of the spin-flip coupling the TMR becomes negative
provided the ferromagnetic polarization is larger than some critical value.
Finally we show how the full knowledge of the transient response allows for
enhancing the spin-current by properly tuning the period of a pulsed bias.
