  We consider self-avoiding walks terminally attached to a surface at which
they can adsorb. A force is applied, normal to the surface, to desorb the walk
and we investigate how the behaviour depends on the vertex of the walk at which
the force is applied. We use rigorous arguments to map out some features of the
phase diagram, including bounds on the locations of some phase boundaries, and
we use Monte Carlo methods to make quantitative predictions about the locations
of these boundaries and the nature of the various phase transitions.
