  In this work we have studied the singular behaviour of gravitational theories
with non symmetric connections. For this purpose we introduce a new criteria
for the appearance of singularities based on the existence of black/white hole
regions of arbitrary codimension defined inside a spacetime of arbitrary
dimension. We discuss this prescription by increasing the complexity of the
particular torsion theory under study. In this sense, we start with
Teleparallel Gravity, then we analyse Einstein-Cartan theory, and finally
dynamical torsion models.
