  We discuss the formation of antihydrogen atoms ($\bar{\rm H}$) in an
ultra-cold positron-antiproton plasma. For positron densities $n_p\agt 10^8$
cm$^{-3}$ the characteristic formation time of stable $\bar{H}$ is determined
by collisional relaxation of highly excited atoms produced in the process of
3-body Thompson recombination. Relying on the mechanisms of ``replacement
collisions'' and ``transverse collisional drift'' we find a bottleneck in the
relaxation kinetics and analyze the physical consequences of this phenomenon.
