We study the support properties of Dirichlet process{based models for
sets of predictor{dependent probability distributions. Exploiting the connection
between copulas and stochastic processes, we provide an alternative de¯nition of
MacEachern's dependent Dirichlet processes. Based on this de¯nition, we provide
su±cient conditions for the full weak support of di®erent versions of the process. In
particular, we show that under mild conditions on the copula functions, the version
where only the support points or the weights are dependent on predictors have full
weak support. In addition, we also characterize the Hellinger and Kullback{Leibler
support of mixtures induced by the di®erent versions of the dependent Dirichlet
process. A generalization of the results for the general class of dependent stick{
breaking processes is also provided.