  Sequence heterogeneity broadens the binding transition of a polymer onto a
linear or planar substrate. This effect is analyzed in a real-space
renormalization group scheme designed to capture the statistics of rare events.
In the strongly disordered regime, binding initiates at an exponentially rare
set of ``good contacts''. Renormalization of the contact potential yields a
Kosterlitz-Thouless type transition in any dimension. This and other
predictions are confirmed by extensive numerical simulations of a directed
polymer interacting with a columnar defect.
