  Using data from Gaia DR2, we study the radial number density profiles of the
Galactic globular cluster sample. Proper motions are used for accurate
membership selection, especially crucial in the cluster outskirts. Due to the
severe crowding in the centres, the Gaia data is supplemented by literature
data from HST and surface brightness measurements, where available. This
results in 81 clusters with a complete density profile covering the full tidal
radius (and beyond) for each cluster. We model the density profiles using a set
of single-mass models ranging from King and Wilson models to generalised
lowered isothermal limepy models and the recently introduced spes models, which
allow for the inclusion of potential escapers. We find that both King and
Wilson models are too simple to fully reproduce the density profiles, with King
(Wilson) models on average underestimating(overestimating) the radial extent of
the clusters. The truncation radii derived from the limepy models are similar
to estimates for the Jacobi radii based on the cluster masses and their orbits.
We show clear correlations between structural and environmental parameters, as
a function of Galactocentric radius and integrated luminosity. Notably, the
recovered fraction of potential escapers correlates with cluster pericentre
radius, luminosity and cluster concentration. The ratio of half mass over
Jacobi radius also correlates with both truncation parameter and PE fraction,
showing the effect of Roche lobe filling.
