  The main astronomical source of r-process elements has not yet been
identified. One plausible site is neutron star mergers (NSMs), but from
perspective of the Galactic chemical evolution, it has been pointed out that
NSMs cannot reproduce the observed r-process abundance distribution of
metal-poor stars at [Fe/H] $< -3$. Recently, Tsujimoto & Shigeyama (2014)
pointed out that NSM ejecta can spread into much larger volume than ejecta from
a supernova. We re-examine the enrichment of r-process elements by NSMs
considering this difference in propagation using the chemical evolution model
under the hierarchical galaxy formation. The observed r-process enhanced stars
around [Fe/H] $\sim -3$ are reproduced if the star formation efficiency is
lower for low-mass galaxies under a realistic delay time distribution for NSMs.
We show that a significant fraction of NSM ejecta escape from its host
proto-galaxy to pollute intergalactic matter and other proto-galaxies. The
propagation of r-process elements over proto-galaxies changes the abundance
distribution at [Fe/H] $< -3$ and obtains distribution compatible with
observations of the Milky Way halo stars. In particular, the pre-enrichment of
intergalactic medium explains the observed scarcity of EMP stars without Ba and
abundance distribution of r-process elements at [Fe/H] $\lesssim -3.5$.
