  We have performed an ab initio investigation of the energetic stability, and
the electronic properties of transition metals (TMs = Mn, Fe, Co, and Ru)
adsorbed on graphene upon the presence of grain boundaries (GBs). Our results
reveal an energetic preference for the TMs lying along the GB sites (TM/GB).
Such an energetic preference has been strengthened by increasing the
concentration of the TM adatoms; giving rise to TM nanolines on graphene ruled
by GBs. Further diffusion barrier calculations for Fe adatoms support the
formation of those TM nanolines. We find that the energy barriers parallel to
the GBs are sligthly lower in comparision with those obtained for the defect
free graphene; whereas, perpendicularly to the GBs the Fe adatoms face higher
energy barriers. Fe and Co (Mn) nanolines are ferromagnetic (ferrimagnetic), in
contrast the magnetic state of Ru nanolines is sensitive to the Ru/GB
adsorption geometry. The electronic properties of those TM nanolines were
characterized through extensive electronic band structure calculations. The
formation of metallic nanolines is mediated by a strong hybridization between
the TM and the graphene ($\pi$) orbitals along the GB sites. Due to the net
magnetization of the TM nanolines, our band structure results indicate an
anisotropic (spin-polarized) electronic current for some TM/GB systems.
