  Giant planets are thought to form by runaway gas accretion onto solid cores.
Growth must eventually stop running away, ostensibly because planets open gaps
(annular cavities) in their surrounding discs. Typical models stop runaway by
artificially capping the accretion rate and lowering it to zero over an
arbitrarily short time-scale. In reality, post-runaway accretion persists as
long as the disc remains. During this final and possibly longest phase of
formation, when the planet is still emerging from the disc, its mass can more
than double, and its radius contracts by orders of magnitude. By drawing from
the theory of how gaps clear, we find that post-runaway accretion luminosities
diverge depending on disc viscosity: luminosities fall in low-viscosity discs
but continue to rise past runaway in high-viscosity discs. This divergence
amounts to a factor of $10^2$ by the time the disc disperses. Irrespective of
the specifics of how planets interact with discs, the observed luminosity and
age of an accreting planet can be used to calculate its instantaneous mass,
radius, and accretion rate. We perform this exercise for the planet candidates
embedded within the discs orbiting PDS 70, HD 163296, and MWC 758, inferring
masses of $1-10\, M_{\rm J}$, accretion rates of $0.1-10\, M_{\rm J}$/Myr, and
radii of $1-10\, R_{\rm J}$. Our radii are computed self-consistently from the
planet's concurrent contraction and accretion and do not necessarily equal the
value of $2R_{\rm J}$ commonly assumed; in particular, the radius depends on
the envelope opacity as $R \propto \kappa^{0.5}$.
