  We construct relative moduli spaces of semistable pairs on a family of
projective Deligne-Mumford stacks. We define moduli stacks of stable orbifold
Pandharipande-Thomas pairs on stacks of expanded degenerations and pairs, and
then show they are separated and proper Deligne-Mumford stacks of finite type.
As an application, we present the degeneration formula for the absolute and
relative orbifold Pandharipande-Thomas invariants.
