  In this paper, we develop the blow-up analysis and establish the energy
quantization for solutions to super-Liouville type equations on Riemann
surfaces with conical singularities at the boundary. In other problems in
geometric analysis, the blow-up analysis usually strongly utilizes conformal
invariance, which yields a Noether current from which strong estimates can be
derived. Here, however, the conical singularities destroy conformal invariance.
Therefore, we develop another, more general, method that uses the vanishing of
the Pohozaev constant for such solutions to deduce the removability of boundary
singularities.
