  We consider the dimerized spin-1 $XXZ$ chain with single-ion anisotropy $D$.
In absence of an explicit dimerization there are three phases: a large-$D$, an
antiferromagnetically ordered and a Haldane phase. This phase structure
persists up to a critical dimerization, above which the Haldane phase
disappears. We show that for weak dimerization the phases are separated by
Gaussian and Ising quantum phase transitions. One of the Ising transitions
terminates in a critical point in the universality class of the dilute Ising
model. We comment on the relevance of our results to experiments on
quasi-one-dimensional anisotropic spin-1 quantum magnets.
