  We study polymer layers formed by irreversible adsorption from a polymer
melt. Our theory describes an experiment which is a ``slow'' version of that
proposed by Guiselin [Europhys. Lett., v. 17 (1992) p. 225] who considered
instantaneously irreversibly adsorbing chains and predicted a universal density
profile of the layer after swelling with solvent to produce the ``Guiselin
brush.'' Here we ask what happens when adsorption is not instantaneous. The
classic example is chemisorption. In this case the brush is formed slowly and
the final structure depends on the experiment's duration, $t_{final}$. We find
the swollen layer consists of an inner region of thickness $z^* \sim
t_{final}^{-5/3}$ with approximately constant density and an outer region
extending up to height $h \sim N^{5/6}$ which has the same density decay $\sim
z^{-2/5}$ as for the Guiselin case.
