The atmospheres of small, close-in exoplanets are vulnerable to rapid mass loss during protoplanetary disc dispersal via a process
referred to as ‘boil-off’, in which confining pressure from the local gas disc reduces, inducing atmospheric loss and contraction.
We construct self-consistent models of planet evolution during gaseous core accretion and boil-off. As the surrounding disc gas
dissipates, we find that planets lose mass via subsonic breeze outflows which allow causal contact to exist between disc and
planet. Planets initially accrete of order ∼ 10 per cent in atmospheric mass, however, boil-off can remove 90 per cent of this
mass during disc dispersal. We show that a planet’s final atmospheric mass fraction is strongly dictated by the ratio of cooling
time-scale to disc dispersal time-scale, as well as the planet’s core mass and equilibrium temperature. With contributions from
core cooling and radioactivity, we show that core luminosity eventually leads to the transition from boil-off to core-powered
mass loss. We find that smaller mass planets closest to their host star may have their atmospheres completely stripped through
a combination of boil-off and core-powered mass loss during disc dispersal, implying the existence of a population-level radius
gap emerging as the disc disperses. We additionally consider the transition from boil-off/core-powered mass loss to X-ray and
extreme ultraviolet (XUV) photoevaporation by considering the penetration of stellar XUV photons below the planet’s sonic
surface. Finally, we show that planets may open gaps in their protoplanetary discs during the late stages of boil-off, which may
enhance mass-loss rates.