  A self-interacting polymer with one end attached to a sticky surface has been
studied by means of a flat-histogram stochastic growth algorithm known as
FlatPERM. We examined the four-dimensional parameter space of the number of
monomers up to 91, self-attraction, surface attraction and force applied to an
end of the polymer. Using this powerful algorithm the \emph{complete} parameter
space of interactions and force has been considered. Recently it has been
conjectured that a hierarchy of states appears at low temperature/poor solvent
conditions where a polymer exists in a finite number of layers close to a
surface. We find re-entrant behaviour from a stretched phase into these
layering phases when an appropriate force is applied to the polymer. We also
find that, contrary to what may be expected, the polymer desorbs from the
surface when a sufficiently strong critical force is applied and does
\emph{not} transcend through either a series of de-layering transitions or
monomer-by-monomer transitions.
