  We analyze a possibility of quantum criticality (gaplessness) in dimerized
antiferromagnetic two- and three-leg spin-1/2 ladders. Contrary to earlier
studies of these models, we examine different dimerization patterns in the
ladder. We find that ladders with the columnar dimerization order have lower
zero-temperature energies and they are always gapped. For the staggered
dimerization order, we find the quantum critical lines, in agreement with
earlier analyses. The bond mean-field theory we apply, demonstrates its
quantitative accuracy and agrees with available numerical results. We conclude
that unless some mechanism for locking dimerization into the energetically less
favorable staggered configuration is provided, the dimerized ladders do not
order into the phase where the quantum criticality occurs.
