I spent this evening reading carefully the important (though now somewhat out-of-date) paper on galaxy growth by merging and accretion in numerical simulations by Murali et al (2002). Unfortunately, the article gives its results entirely in terms of the volume average of the merger rate over all galaxy masses and types, when the per-galaxy growth rate might be a more stable (and definitely more easily testable) statistic. The paper finds that the merger rate as measured observationally is consistent with their findings, though the test would be more sensitive if they had produced and tested per-galaxy numbers. However, they find that for massive galaxies, the smooth accretion rate of intergalactic material is substantially larger than the galaxy merger rate (in mass per time units); I think this is not consistent with present-day observations (although it is hard to test definitively if the IGM material is ionized).
Despite the great improvement in both observations and simulations, there is a surprising paucity of good theoretical predictions for the merger rate since this nice paper.