We present a study of galaxy mergers up to $z=10$ using the Planck Millennium cosmological dark matter simulation and the {tt GALFORM} semi-analytical model of galaxy formation. Utilising the full ($800$ Mpc)$^3$ volume of the simulation, we studied the statistics of galaxy mergers in terms of merger rates and close pair fractions. We predict that merger rates begin to drop rapidly for high-mass galaxies ($M_*>10^{11.3}-10^{10.5}$ $M_odot$ for $z=0-4$), as a result of the exponential decline in the galaxy stellar mass function. The predicted merger rates increase and then turn over with increasing redshift, in disagreement with the Illustris and EAGLE hydrodynamical simulations. In agreement with most other models and observations, we find that close pair fractions flatten or turn over at some redshift (dependent on the mass selection). We conduct an extensive comparison of close pair fractions, and highlight inconsistencies among models, but also between different observations. We provide a fitting formula for the major merger timescale for close galaxy pairs, in which the slope of the stellar mass dependence is redshift dependent. This is in disagreement with previous theoretical results that implied a constant slope. Instead we find a weak redshift dependence only for massive galaxies ($M_*>10^{10}$ M$_odot$): in this case the merger timescale varies approximately as $M_*^{-0.55}$. We find that close pair fractions and merger timescales depend on the maximum projected separation as $r_mathrm{max}^{1.35}$. This is in agreement with observations of small-scale clustering of galaxies, but is at odds with the linear dependence on projected separation that is often assumed.
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