  In the local Universe, the existence of very young galaxies (VYGs), having
formed at least half their stellar mass in the last 1 Gyr, is debated. We
predict the present-day fraction of VYGs among central galaxies as a function
of galaxy stellar mass. For this, we apply to high mass resolution Monte-Carlo
halo merger trees (MCHMTs) three (one) analytical models of galaxy formation,
where the ratio of stellar to halo mass (mass growth rate) is a function of
halo mass and redshift. Galaxy merging is delayed until orbital decay by
dynamical friction. With starbursts associated with halo mergers, our models
predict typically one percent of VYGs up to galaxy masses of $10^{10}$
M$_\odot$, falling rapidly at higher masses, and VYGs are usually associated
with recent major mergers of their haloes. Without these starbursts, two of the
models have VYG fractions reduced by 1 or 2 dex at low or intermediate stellar
masses, and VYGs are rarely associated with major halo mergers. In comparison,
the state-of-the-art semi-analytical model (SAM) of Henriques et al. produces
only 0.01% of VYGs at intermediate masses. Finally, the Menci et al. SAM run on
MCMHTs with Warm Dark Matter cosmology generates 10 times more VYGs at masses
below $10^8$ M$_\odot$ than when run with Cold Dark Matter. The wide range in
these VYG fractions illustrates the usefulness of VYGs to constrain both galaxy
formation and cosmological models.
