  We study the branch divisors on the boundary of the canonical toroidal
compactification of ball quotients. We show a criterion, the low slope cusp
form trick, for proving that ball quotients are of general type. Moreover, we
classify when irregular cusps exist in the case of the discriminant kernel and
construct concrete examples for some arithmetic subgroups. As another direction
of study, when a complex ball is embedded into a Hermitian symmetric domain of
type IV, we determine when regular or irregular cusps map to regular or
irregular cusps studied by Ma.
