  We use a large sample of $\sim 350,000$ galaxies constructed by combining the
UKIDSS UDS, VIDEO/CFHT-LS, UltraVISTA/COSMOS and GAMA survey regions to probe
the major merging histories of massive galaxies ($>10^{10}\ \mathrm{M}_\odot$)
at $0.005 < z < 3.5$. We use a method adapted from that presented in
Lopez-Sanjuan et al. (2014) using the full photometric redshift probability
distributions, to measure pair $\textit{fractions}$ of flux-limited, stellar
mass selected galaxy samples using close-pair statistics. The pair fraction is
found to weakly evolve as $\propto (1+z)^{0.8}$ with no dependence on stellar
mass. We subsequently derive major merger $\textit{rates}$ for galaxies at $>
10^{10}\ \mathrm{M}_\odot$ and at a constant number density of $n > 10^{-4}$
Mpc$^{-3}$, and find rates a factor of 2-3 smaller than previous works,
although this depends strongly on the assumed merger timescale and likelihood
of a close-pair merging. Galaxies undergo approximately 0.5 major mergers at $z
< 3.5$, accruing an additional 1-4 $\times 10^{10}\ \mathrm{M}_\odot$ in the
process. Major merger accretion rate densities of $\sim 2 \times 10^{-4}$
$\mathrm{M}_\odot$ yr$^{-1}$ Mpc$^{-3}$ are found for number density selected
samples, indicating that direct progenitors of local massive
($>10^{11}\mathrm{M}_\odot$) galaxies have experienced a steady supply of
stellar mass via major mergers throughout their evolution. While pair fractions
are found to agree with those predicted by the Henriques et al. (2014)
semi-analytic model, the Illustris hydrodynamical simulation fails to
quantitatively reproduce derived merger rates. Furthermore, we find major
mergers become a comparable source of stellar mass growth compared to
star-formation at $z < 1$, but is 10-100 times smaller than the SFR density at
higher redshifts.
