We investigate formation processes and physical properties of globular cluster systems (GCSs) in galaxies based on high-resolution cosmological simulations with globular clusters. We focus on metal-poor clusters (MPCs) and correlations with their host galaxies by assuming that MPC formation is truncated at a high redshift (z_trun > 6). We find that the correlation between mean metallicities (Z_gc) of MPCs and their host galaxy luminosities (L) flattens from z=z_trun to z=0. We also find that the observed relation (Z_gc ~ L^0.15) in MPCs can be reproduced well in the models with Z_gc ~ L^0.5 at z=z_trun when z_trun ~ 10, if mass-to-light-ratios are assumed to be constant at z=z_trun. However, better agreement with the observed relation is found for models with different mass-to-light-ratios between z=z_trun and z=0. It is also found that the observed color-magnitude relation of luminous MPCs (i.e., ``blue tilts) may only have a small contribution from the stripped stellar nuclei of dwarf galaxies, which have nuclei masses that correlate with their total mass at z=z_trun. The simulated blue tilts are found to be seen more clearly in more massive galaxies, which reflects the fact that more massive galaxies at z=0 are formed from a larger number of dwarfs with stellar nuclei formed at z>z_trun. The half-number radii (R_e) of GCSs, velocity dispersions of GCSs (sigma), and their host galaxy masses (M_h) are found to be correlated with one another such that R_e ~ M_h^{0.57} and sigma ~ M_h^{0.32}.
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