We use Horizon-AGN, a hydrodynamical cosmological simulation, to explore the role of mergers in the evolution of massive (M > 10^10 MSun) galaxies around the epoch of peak cosmic star formation (1<z<4). The fraction of massive galaxies in major mergers (mass ratio R<4:1) is around 3%, a factor of ~2.5 lower than minor mergers (4:1<R <10:1) at these epochs, with no trend with redshift. At z~1, around a third of massive galaxies have undergone a major merger, while all such systems have undergone either a major or minor merger. While almost all major mergers at z>3 are blue (i.e. have significant associated star formation), the proportion of red mergers increases rapidly at z<2, with most merging systems at z~1.5 producing remnants that are red in rest-frame UV-optical colours. The star formation enhancement during major mergers is mild (~20-40%) which, together with the low incidence of such events, implies that this process is not a significant driver of early stellar mass growth. Mergers (R < 10:1) host around a quarter of the total star formation budget in this redshift range, with major mergers hosting around two-thirds of this contribution. Notwithstanding their central importance to the standard LCDM paradigm, mergers are minority players in driving star formation at the epochs where the bulk of todays stellar mass was formed.
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