Using both analytic theory and computer simulation we study the stretching
along the surface of a strongly adsorbed polymer chain. In marked contrast
to the case of nonadsorbed chains we show that the polymer does not undergo
a Rayleigh instability. Instead it deforms steadily into a lens shape. Our
results have dramatic consequences for submonolayer films formed from graf
ted chains. We show that strongly adsorbed chains do not form "octopus" or
pinned micelles. Instead they fuse into compact islands, which in the limit
of high grafting density can form a continuous network. [S0031-9007(99)087
83-9].