  We prove that parabolic uniformly rectifiable sets admit (bilateral) corona
decompositions with respect to regular Lip(1,1/2) graphs. Together with our
previous work, this allows us to conclude that if
$\Sigma\subset\mathbb{R}^{n+1}$ is parabolic Ahlfors-David regular, then the
following statements are equivalent.
  (1) $\Sigma$ is parabolic uniformly rectifiable.
  (2) $\Sigma$ admits a corona decomposition with respect to regular Lip(1,1/2)
graphs.
  (3) $\Sigma$ admits a bilateral corona decomposition with respect to regular
Lip(1,1/2) graphs.
  (4) $\Sigma$ is big pieces squared of regular Lip(1,1/2) graphs.
