  SDSSJ1049+5103, commonly known as Willman 1, is an extremely low-luminosity
Milky Way companion whose properties are intermediate between those of globular
clusters and dwarf spheroidals. In this paper, we use deep photometry to show
that this object is old and moderately metal-poor, has a distance of 38 +/- 7
kpc, has an M_V of -2.5 mag, and has a half-light radius of 21 +/- 7 pc,
consistent with previous estimates. The spatial distribution of Willman 1's
main sequence stars shows 1) its total spatial extent exceeds its tidal radius
for a range of assumptions about its total mass and its orbit and 2) the
presence of prominent multi-directional stellar tails. The tidal interactions
causing these tail features may explain the large physical size of Willman 1
relative to low-luminosity globular clusters. It is the most distant Galactic
object yet known to display prominent tails, and is the only distant satellite
to display multi-directional tails. Although we cannot at present determine the
cause of this unusual morphology, preliminary comparisons between the
morphology of Willman 1 and published simulations suggest that it may be near
the apocenter of its orbit, or that it may have interacted with another halo
object. We find a significant difference between the luminosity functions of
stars in the center and in the tails of Willman 1, strongly suggesting mass
segregation much like that seen in Palomar 5. Although Willman 1 has more
pronounced tidal tails than most confirmed Milky Way dwarf galaxies, because of
its very low stellar mass we cannot at present rule out the possibility that it
has a dark matter halo. (Abridged)
