  We study the evolution of globular cluster systems (GCS) in elliptical
galaxies and explore the dependence of their main properties on the mass and
the size of the host galaxy.The dependence of the evolution of the GCS mass
function (GCMF), of the fraction of surviving clusters and of the ratio of the
final to initial mass in clusters on the structure of the host galaxy as well
as their variation with the galactocentric distance inside individual host
galaxies has been thoroughly investigated.After a survey over a large number of
different host galaxies we have restricted our attention to a sample of
galaxies with effective masses and radii equal to those observed for
dwarf,normal and giant ellipticals. We show that, in spite of large differences
in the fraction of surviving clusters, the final mean masses of the GCMF in
massive galaxies are very similar to each other with a small galaxy-to-galaxy
dispersion;low-mass compact galaxies tend to have smaller values of the final
mean mass and a larger galaxy-to-galaxy dispersion. These findings are in
agreement with those of recent observational analyses. The fraction of
surviving clusters increases with the mass of the host galaxy. We show that a
small difference between the initial and the final mean mass and dispersion of
the GCMF and the lack of a significant radial dependence of the mean mass
inside individual galaxies do not necessarily imply that evolutionary processes
have been unimportant in the evolution of the initial population of clusters.
For giant galaxies most disruption occurs within the effective radius while for
low-mass galaxies a significant disruption of clusters takes place also at
larger galactocentric distances. The dependence of the results obtained on the
initial mean mass of the GCMF is investigated. (abridged)
