  We performed an extended analysis of the parameter space for the interaction
of the Magellanic System with the Milky Way (MW). The varied parameters cover
the phase space parameters, the masses, the structure, and the orientation of
both Magellanic Clouds, as well as the flattening of the dark matter halo of
the MW. The analysis was done by a specially adopted optimization code
searching for the best match between numerical models and the detailed HI map
of the Magellanic System by Bruens et al. (2005). The applied search algorithm
is a genetic algorithm combined with a code based on the fast, but
approximative restricted N-body method. By this, we were able to analyze more
than 10^6 models, which makes this study one of the most extended ones for the
Magellanic System. Here we focus on the flattening q of the axially symmetric
MW dark matter halo potential, that is studied within the range 0.74<=q<=1.20.
We show that creation of a trailing tail (Magellanic Stream) and a leading
stream (Leading Arm) is quite a common feature of the Magellanic System-MW
interaction, and such structures were modeled across the entire range of halo
flattening values. However, important differences exist between the models,
concerning density distribution and kinematics of HI, and also the dynamical
evolution of the Magellanic System. Detailed analysis of the overall agreement
between modeled and observed distribution of neutral hydrogen shows that the
models assuming an oblate (q<1.0) dark matter halo of the Galaxy allow for
better satisfaction of HI observations than models with other halo
configurations.
