  We present a deep photometric survey of M31, conducted with the CFHT and INT,
covering the inner 50 kpc of the galaxy, the Southern quadrant out to 150 kpc,
and extending to M33. This is the first systematic panoramic study of this very
outermost region of galaxies. We detect several streams and other large-scale
structures, and two new dwarf galaxies: And XV and XVI. The discovery of
substructure on the minor axis, together with the fact that the light profile
between 0.5 < R < 1.3 follows the exponential ``extended disk'', is
particularly important in shedding light on the mixed and sometimes conflicting
results reported in previous studies. Underlying the substructures lies a
faint, metal-poor, smooth and extremely extended halo, reaching out to at least
150 kpc. The smooth halo component in M31 has a profile that can be fit with a
Hernquist model of immense scale radius ~55 kpc, almost a factor of 4 larger
than theoretical predictions. Alternatively a power-law with exponent -1.91 +/-
0.11 can be fit to the profile. The total luminosity of this structure is
similar to that of the halo of the Milky Way. This vast, smooth, underlying
halo is reminiscent of a classical monolithic model and completely unexpected
from modern galaxy formation models. M33 is also found to have an extended
metal-poor halo component, which can be fit with a Hernquist model also of
scale radius ~55 kpc. These extended slowly-decreasing halos will provide a
challenge and strong constraints for further modeling. [Abridged]
