Moduli of surfaces fibered in log Calabi-Yau pairs

We study the moduli spaces of surface pairs admitting a log Calabi--Yau fibration . We develop a series of results on stable reduction and apply them to give an explicit description of the boundary of the KSBA compactification. Three interesting cases where our results apply are: (1) divisors on of bidegree ; (2) K3 surfaces which map to , with and the ramification locus, or (3) elliptic surfaces with either a section or a bisection. The main tools employed are stable quasimaps, the canonical bundle formula, and the minimal model program.