  The universal, scaled order parameter profiles $P_{\pm}(z/\xi)$ for critical
adsorption of a fluid or fluid mixture onto a wall or interface, and for the
extraordinary transition of the semi-infinite Ising model, are discussed
theoretically, where $z$ is the distance from the interface, $\xi (T)$ is the
bulk correlation length, and the subscript $+$ ($-$) refers to the approach
from above (below) $T_c$. Recent results to first order in the $\epsilon=4-d$
expansion are extrapolated to $d=3$ space dimensions and compared with new
Monte Carlo results. In order to obtain meaningful extrapolations it is crucial
that both the exponential decay at large $\zeta$ as well as the known algebraic
behavior $P_{\pm}(\zeta)\sim\zeta^{-\beta/\nu}$ at small $\zeta$ be correctly
reproduced. To this end a recently developed novel RG scheme involving a $z$
dependent amplitude renormalization is used. Reasonable agreement of our
extrapolations with the Monte Carlo results and some experimental results is
obtained.
