  We consider spin-half quantum antiferromagnets in two spatial dimensions in
the quantum limit, where the spins are in a valence bond solid (VBS) phase. The
transitions between two such VBS phases is studied. In some cases, an
interesting second order transition controlled by a fixed line with varying
critical exponents if found. A specific example is provided by an
antiferromagnetically coupled bilayer system on the honeycomb lattice where a
continuous quantum phase transition can generically exist between two VBS
phases. Furthermore, these critical points are deconfined, in the sense that
gapped spin-1/2 spinon excitations emerge right at the transition. The low
energy physics of this critical point (upto marginally irrelevant interactions)
contains just a free quadratically dispersing `photon'. The phase structure on
one side of this continuous transition is very intricate consisting of a series
of infinitely closely spaced further transitions in a `devil's staircase' form.
Analogies with previous examples of deconfined quantum criticality are
emphasized. Closely related transitions in single layer systems are explored.
These are second order only at some multicritical points. The solvable
Rokshar-Kivelson point of quantum dimer models of single layer systems is found
to correspond to a very special non-generic multicritical point
