  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 today's stellar mass was formed.
