Population III stars around the Milky Way
  We explore the possibility of observing Population III (Pop~III) stars, born
of the primordial gas.
  Pop~III stars with masses below $0.8 M_\odot$ should survive to date though
are not observed yet, but the existence of stars with low metallicity as
[Fe/H]$ < -5$ in the Milky Way halo suggests the surface pollution of Pop~III
stars with accreted metals from the interstellar gas after birth. In this
paper, we investigate the runaway of Pop~III stars from their host mini-halos,
considering the ejection of secondary members from binary systems when their
massive primaries explode as supernovae.
  These stars save them from the surface pollution.
  By computing the star formation and chemical evolution along with the
hierarchical structure formation based on the extended Press--Schechter merger
trees, we demonstrate that several hundreds to tens of thousands of low-mass
Pop~III stars escape from the building blocks of the Milky Way.
  The second and later generations of extremely metal-poor (EMP) stars are also
escaped from the mini-halos.
  We discuss the spatial distributions of these escaped stars by evaluating the
distances between the mini-halos in the branches of merger trees under the
spherical collapse model of dark matter halos.
  It is demonstrated that the escaped stars distribute beyond the stellar halo
with a density profile close to the dark matter halo, while the Pop~III stars
are slightly more centrally concentrated .
  Some escaped stars leave the Milky Way and spread into the intergalactic
space.
  Based on the results, we discuss the feasibility of observing the Pop~III
stars with the pristine surface abundance.
