The absorption of free linear chains in a polymer brush was studied with respect to chain size and compatibility with the brush by means of Monte Carlo simulations and Density Functional Theory / Self-Consistent Field Theory at both moderate and high grafting densities using a bead-spring model. Different concentrations of the free chains were examined. When free chains are incompatible with the brush, all oligomeric species are almost completely ejected by the polymer brush irrespective of their length. For compatible case, we find that in going from shorter to longer chains, the absorbed amount undergoes a sharp crossover from weak to strong absorption. For a moderately dense brush, the longer species populate predominantly the deep inner part of the brush whereas in a dense brush they penetrate into the tail of the brush only. The penetration/expulsion kinetics of free chains into the polymer brush after an instantaneous change in their compatibility displays a rather rich behavior. We find three distinct regimes of penetration kinetics of free chains whereby the time of absorption grows with the chain length at a different rate. During the initial stages of penetration into the brush one observes a power-law increase of the absorbed amount as a function of time.