  Approximately once every $10^4$ years, a star passes close enough to the
supermassive black hole Sgr A* at the center of the Milky Way to be pulled
apart by the black hole's tidal forces. The star is then "spaghettified" into a
long stream of matter, with approximately one half being bound to Sgr A* and
the other half unbound. Within this stream, the local self-gravity dominates
the tidal field of Sgr A*, which at minimum restricts the stream to a small
finite width. As the stream cools from adiabatic expansion and begins to
recombine, the residual self-gravity allows for planetary-mass fragments to
form along the length of the stream; these fragments are then shot out into the
galaxy at range of velocities, with the fastest moving at ~10% c. We determine
the phase space distributions of these fragments for a realistic ensemble of
stellar disruptions, along with the local density of fragments in the solar
neighborhood. We find that ~$10^7$ fragments produced by Sgr A* accumulate
within the Milky Way over its lifetime, that there are ~$10^7$ fragments that
lie within 1 Mpc of the Milky Way originating from other galaxies, and that the
nearest fragment to our Sun is on average 500 pc distant.
