  We study the question of how the competition between $\textit{bulk disorder}$
and a $\textit{localized microscopic defect}$ affects the macroscopic behavior
of a system in the directed polymer context at the free energy level. We
consider the directed polymer model on a disordered $d$-ary tree and represent
the localized microscopic defect by modifying the disorder distribution at each
vertex in a single path (branch), or in a subtree, of the tree. The polymer
must choose between following the microscopic defect and finding the best
branches through the bulk disorder. We describe three possible phases, called
the $\textit{fully pinned, partially pinned}$ and $\textit{depinned}$ phases.
When the microscopic defect is associated only with a single branch, we compute
the free energy and the critical curve of the model, and show that the
partially pinned phase does not occur. When the localized microscopic defect is
associated with a non-disordered regular subtree of the disordered tree, the
picture is more complicated. We prove that all three phases are non-empty below
a critical temperature, and that the partially pinned phase disappears above
the critical temperature.
