  Let k be a positive integer and let D_k denote the space of joint
distributions for k-tuples of selfadjoint elements in C*-probability space. The
paper studies the concept of "subordination distribution of \mu \boxplus \nu
with respect to \nu" for \mu, \nu \in D_k, where \boxplus is the operation of
free additive convolution on D_k. The main tools used in this study are
combinatorial properties of R-transforms for joint distributions and a related
operator model, with operators acting on the full Fock space
  Multi-variable subordination turns out to have nice relations to a process of
evolution towards \boxplus-infinite divisibility on D_k that was recently found
by Belinschi and Nica (arXiv:0711.3787). Most notably, one gets better insight
into a connection which this process was known to have with free Brownian
motion.
