  We study stellar and black hole mass assembly in a sample of 42
infrared-luminous galaxy mergers at z<0.3 by combining results from radiative
transfer modelling with archival measures of molecular gas and black hole mass.
The ratios of stellar mass, molecular gas mass, and black hole mass to each
other are consistent with those of massive gas-rich galaxies at z<0.3. The
advanced mergers may show increased black hole mass to stellar mass ratios,
consistent with the transition from AGN to ellipticals and implying substantial
black hole mass growth over the course of the merger. Star formation rates are
enhanced relative to the local main sequence, by factors of ~100 in the
starburst and ~1.8 in the host. The starburst star formation rates appear
distinct to star formation in the main sequence at all redshifts up to at least
z~5. Starbursts may prefer late-stage mergers, but are observed at any merger
stage. We do not find evidence that the starbursts in these low-redshift
systems substantially increase the total stellar mass, with a soft upper limit
on the stellar mass increase from starburst activity of about a factor of two.
In contrast, 12 objects show evidence for super-Eddington accretion, associated
with late-stage mergers, suggesting that many AGN in infrared-luminous mergers
go through a super-Eddington phase. The super-Eddington phase may increase
black hole mass by up to an order of magnitude at an accretion efficiency of
42+/-33% over a period of 44+/-22Myr. Our results imply that super-Eddington
accretion is an important black hole growth channel in infrared-luminous
galaxies at all redshifts.
