  The subsequent coalescence of low--mass halos over cosmic time is thought to
be the major formation channel of massive spiral galaxies like the Milky Way
and the Andromeda Galaxy (M31). The gaseous halo of a massive galaxy is
considered to be the reservoir of baryonic matter persistently fueling the star
formation in the disk. Because of its proximity, M31 is the ideal object for
studying the structure of the halo gas in great detail. Using the latest
neutral atomic hydrogen (HI) data of the Effelsberg-Bonn HI Survey (EBHIS)
allows comprising a comprehensive inventory of gas associated with M31. The
primary aim is to differentiate between physical structures belonging to the
Milky Way Galaxy and M31 and accordingly to test the presence of a M31 neutral
gaseous halo. Analyzing the spatially fully sampled EBHIS data makes it
feasible to trace coherent HI structures in space and radial velocity. To
disentangle Milky Way and M31 HI emission we use a new approach, along with the
traditional path of setting an upper radial velocity limit, by calculating a
difference second moment map. We argue that M31's disk is physically connected
to an asymmetric HI halo of tens of kpc size, the M31 cloud. We confirm the
presence of a coherent low-velocity HI filament located in between M31 and M33
aligned at the sky with the clouds at systemic velocity. The physical
parameters of the HI filament are comparable to those of the HI clouds at
systemic velocity. We also detected an irregularly shaped HI cloud that is is
positionally located close to but offset from the stellar body of And XIX.
