  We determine the existence of critical lines in dimerized quantum spin
ladders in their phase diagram of coupling constants using the finite-size DMRG
algorithm. We consider both staggered and columnar dimerization patterns, and
antiferromagnetic and ferromagnetic inter-leg couplings. The existence of
critical phases depends on the precise combination of these patterns. The
nature of the massive phases separating the critical lines are characterized
with generalized string order parameters that determine their valence bond
solid (VBS) content.
