  We study the growth of dark matter halos in the concordance LCDM cosmology
using several N-body simulations of large cosmological volumes. We build merger
trees from the Millennium and Millennium-II simulations, covering a range
10^9-10^15 Msun in halo mass and 1-10^5 in merger mass ratio. Our algorithm
takes special care of halo fragmentation and ensures that the mass contribution
of each merger to halo growth is only counted once. This way the integrated
merger rate converges and we can consistently determine the contribution of
mergers of different mass ratios to halo growth. We find that all resolved
mergers, up to mass ratios of 10^5, contribute only ~60% of the total halo mass
growth, while major mergers are subdominant, e.g. mergers with mass ratios
smaller than 3:1 (10:1) contribute only ~20% (~30%). This is verified with an
analysis of two additional simulation boxes, where we follow all particles
individually throughout cosmic time. Our results are also robust against using
several halo definitions. Under the assumption that the power-law behaviour of
the merger rate at large mass ratios can be extrapolated to arbitrarily large
mass ratios, it is found that, independently of halo mass, ~40% of the mass in
halos comes from genuinely smooth accretion of dark matter that was never bound
in smaller halos. We discuss possible implications of our findings for galaxy
formation. One implication, assuming as is standard that the pristine
intergalactic medium is heated and photoionized by UV photons, is that all
halos accrete >40% of their baryons in smooth "cold" T>~10^4K gas, rather than
as warm, enriched or clumpy gas or as stars.
