  Impact crater counts on the Saturnian satellites are a key element for
estimating their surface ages and placing constraints on their impactor
population. The Cassini mission radar observations allowed crater counts to be
made on the surface of Titan, revealing an unexpected scarcity of impact
craters that show high levels of degradation. Following previous studies on
impact cratering rates on the Saturnian satellites, we modeled the cratering
process on Titan to constrain its surface chronology and to assess the role of
centaur objects as its main impactors. A theoretical model previously developed
was used to calculate the crater production on Titan, considering the centaur
objects as the main impactors and including two different slopes for the
size-frequency distribution (SFD) of the smaller members of their source
population. A simple model for the atmospheric shielding effects is considered
within the cratering process and our results are then compared with other
synthetic crater distributions and updated observational crater counts. This
comparison is then used to compute Titan's crater retention age for each crater
diameter. The cumulative crater distribution produced by the SFD with a
differential index of $s_2 = 3.5$ is found to consistently predict large
craters (D > 50 km) on the surface of Titan, while it overestimates the number
of smaller craters. As both the modeled and observed distributions flatten for
craters with $D \lesssim 25 $ km due to atmospheric shielding, the difference
between them can be considered as a proxy for the scale to which erosion
processes have acted on the surface of Titan throughout the Solar System age.
Our results for the surface chronology of Titan indicate that craters with D >
50 km can prevail over the Solar System age, whereas smaller craters may be
completely obliterated due to erosion processes acting globally.
