  The influence of long-range correlated surface and decaying near surface
disorder with quenched defects is studied. We consider a correlation function
for the defects of the form $\frac{e^{-z/\xi}}{r^{a}}$, where $a<d-1$ and $z$
being the coordinate in the direction perpendicular to the surface and $r$
denotes the distance parallel to the surface. We investigate the process of
adsorption of long-flexible polymer chains with excluded volume interactions on
a "marginal" and attractive wall in the framework of renormalization group
field theoretical approach up to first order of perturbation theory in a double
($\epsilon$,$\delta$)- expansion ($\epsilon=4-d$, $\delta=3-a$) for the
semi-infinite $|\phi|^4$ $O(m,n)$ model with the above mentioned type of
surface and near the surface disorder in the limit $m,n\to 0$. In particular we
study two limiting cases. First, we investigate the scenario where the chain's
extension it much larger then $\xi$. Second, we consider the case where the
chain's extension is of the order of $\xi$. For both cases we obtained series
for bulk and the whole set of surface critical exponents, characterizing the
process of adsorption of long-flexible polymer chains at the surface. The
polymer linear dimensions parallel and perpendicular to the surface and the
corresponding partition functions as well as the behavior of monomer density
profiles and the fraction of adsorbed monomers at the surface and in the volume
are studied.
