  Planet formation occurs over a few Myr within protoplanetary discs of dust
and gas, which are often assumed to evolve in isolation. However, extended
gaseous structures have been uncovered around many protoplanetary discs,
suggestive of late-stage in-fall from the interstellar medium (ISM). To
quantify the prevalence of late-stage in-fall, we apply an excursion set
formalism to track the local density and relative velocity of the ISM over the
disc lifetime. We then combine the theoretical Bondi-Hoyle-Lyttleton (BHL)
accretion rate with a simple disc evolution model, anchoring stellar accretion
time-scales to observational constraints. Disc lifetimes, masses, stellar
accretion rates and gaseous outer radii as a function of stellar mass and age
are remarkably well-reproduced by our simple model that includes only ISM
accretion. We estimate $20{-}70$ percent of discs may be mostly composed of
material accreted in the most recent half of their lifetime, suggesting disc
properties are not a direct test of isolated evolution models. Our calculations
indicate that BHL accretion can also supply sufficient energy to drive
turbulence in the outer regions of protoplanetary discs with viscous
$\alpha_\mathrm{SS} \sim 10^{-5}- 10^{-1}$, although we emphasise that angular
momentum transport and particularly accretion onto the star may still be driven
by internal processes. Our simple approach can be easily applied to
semi-analytic models. Our results represent a compelling case for regulation of
planet formation by large-scale turbulence, with broad consequences for planet
formation theory. This possibility urgently motivates deep observational
surveys to confirm or refute our findings.
