  We develop the moduli theory of boundary polarized CY pairs, which are slc
Calabi-Yau pairs $(X,D)$ such that $D$ is ample. The motivation for studying
this moduli problem is to construct a moduli space at the Calabi-Yau wall
interpolating between certain K-moduli and KSBA moduli spaces. We prove that
the moduli stack of boundary polarized CY pairs is S-complete,
$\Theta$-reductive, and satisfies the existence part of the valuative criterion
for properness, which are steps towards constructing a proper moduli space. A
key obstacle in this theory is that the irreducible components of the moduli
stack are not in general of finite type. Despite this issue, in the case of
pairs $(X,D)$ where $X$ is a degeneration of $\mathbb{P}^2$, we construct a
projective moduli space on which the Hodge line bundle is ample. As a
consequence, we complete the proof of a conjecture of Prokhorov and Shokurov in
relative dimension two.
