  The form of the halo mass function is a basic ingredient in any
semi-analytical galaxy formation model. We study the existing forms of the mass
functions in the literature and compare their predictions for semi-analytical
galaxy formation models. Two methods are used in the literature to compute the
net formation rate of halos, one by simply taking the derivative of the halo
mass function and the other using the prescription due to Sasaki (1994). For
the Press-Schechter (PS) mass function, we compare various model predictions,
using these two methods. However, as the Sasaki formalism cannot be easily
generalized for other mass functions, we use the derivative while comparing
model predictions of different mass functions. We show that the reionization
history and UV luminosity function of Lyman break galaxies (LBGs) predicted by
the PS mass function differs from those using any other existing mass function,
like Sheth-Tormen (ST) mass function.In particular the reionization efficiency
of molecular cooled halos has to be substantially reduced when one uses the ST
and other mass functions obtained from the simulation instead of the PS mass
function. Using $\chi^2$-minimization, we find that the observed UV luminosity
functions of LBGs at $3.0\le z\le 7.4$ are better reproduced by models using
the ST mass function compared to models that use the PS mass function. On the
other hand, the volume filling factor of the metals expelled from the galaxies
through supernovae driven outflows differs very little between models with
different mass functions. It depends on the way we treat merging outflows. We
also show that the porosity weighted average quantities related to the outflow
are not very sensitive to the differences in the halo mass function.
