  We present here new results of two-dimensional hydrodynamical simulations of
the eruptive events of the 1840s (the great) and the 1890s (the minor)
eruptions suffered by the massive star $\eta$ Car. The two bipolar nebulae
commonly known as the Homunculus and the little Homunculus were formed from the
interaction of these eruptive events with the underlying stellar wind. As in
previous work (Gonzalez et al. 2004a, 2004b), we assume here an interacting,
nonspherical multiple-phase wind scenario to explain the shape and the
kinematics of both Homunculi, but adopt a more realistic parametrization of the
phases of the wind. During the 1890s eruptive event, the outflow speed {\it
decreased} for a short period of time. This fact suggests that the little
Homunculus is formed when the eruption ends, from the impact of the
post-outburst $\eta$ Car wind (that follows the 1890s event) with the eruptive
flow (rather than by the collision of the eruptive flow with the pre-outburst
wind, as claimed in previous models; Gonzalez et al. 2004a, 2004b). Our
simulations reproduce quite well the shape and the observed expansion speed of
the large Homunculus. The little Homunculus (which is embedded within the large
Homunculus) becomes Rayleigh-Taylor unstable and develop filamentary structures
that resembles the spatial features observed in the polar caps. In addition, we
find that the interior cavity between the two Homunculi is partially filled by
material that is expelled during the decades following the great eruption. This
result may be connected with the observed double-shell structure in the polar
lobes of the $\eta$ Car nebula. Finally, as in previous work, we find the
formation of tenuous, equatorial, high-speed features that seem to be related
to the observed equatorial skirt of $\eta$ Car.
