We examine the reliability of the merger trees generated for the Monte-Carlo
modeling of galaxy formation. In particular we focus on the cold gas fraction
predicted from the merger trees with different assumptions on the progenitor
distribution function, the timestep, and the mass resolution. We show that the
cold gas fraction is sensitive to the accuracy of the merger trees at
small-mass scales of progenitors at high redshifts. One can reproduce the
Press-Schechter prediction to a reasonable degree by adopting a fairly large
number of redshift bins, N_{step} ~ 1000 in generating merger trees, which is a
factor of ten larger than the canonical value used in previous literature.Comment: 9 pages, 10 figures. To appear in PASJ, October 25, 200