  We have derived the global mass functions of a sample of 35 Galactic globular
clusters by comparing deep Hubble Space Telescope photometry with suitable
multimass dynamical models. For a subset of 29 clusters with available radial
velocity information we were also able to determine dynamical parameters,
mass-to-light ratios and the mass fraction of dark remnants. The derived global
mass functions are well described by single power-laws in the mass range $0.2 <
m/M_\odot < 0.8$ with mass function slopes $\alpha>-1$. Less evolved clusters
show deviations from a single-power law, indicating that the original shape of
their mass distribution was not a power-law. We find a tight anticorrelation
between the present-day mass function slopes and the half-mass relaxation
times, which can be understood if clusters started from the same universal IMF
and internal dynamical evolution is the main driver in shaping the present-day
mass functions. Alternatively, IMF differences correlated with the present-day
half-mass relaxation time are needed to explain the observed correlation. The
large range of mass function slopes seen for our clusters implies that most
globular clusters are dynamically highly evolved, a fact that seems difficult
to reconcile with standard estimates for the dynamical evolution of clusters.
The mass function slopes also correlate with the dark remnant fractions
indicating a preferential retention of massive remnants in clusters subject to
high mass-loss rates.
