We develop a coarse-grained Monte Carlo model for the anchoring of cationic polymers onto a phosphatidyl-choline (PC) lipid monolayer, doped with univalent phosphatidylserine (PS) and tetravalent phosphatidylinositol 4, 5-bisphosphate (PIP2) anionic lipids. Using this model, we extensively explore the effects of important factors on the structural alterations of the polymers/monolayer complex, including the polymer concentration, the polymer ionization fraction and the ionic concentration of the salt solution. We find the substantial disparity in the scaling of the anchoring/dissociation transition for polymers/monolayer complex and polyelectrolyte/surface system, which demonstrates that the mobile anionic monolayer exerts stronger attraction on cationic polymers than uniformly charged surface, thereby illustrating the significant predominance of PIP2 lipids in the anchoring procedure. In the polymer anchoring regime, increasing the polymer ionization fraction drastically strengthens the attractions between polymers and the monolayer at low polymer concentrations, which in turn results in the transformation of individual polymer chains from a brush-like structure to a pancake-like structure and leads to the enhancement of PIP2 sequestration. Elevating the polymer concentration strengthens the competition of the anchoring between individual polymers, and the fraction of anchored polymers can even saturate at sufficiently high polymer concentrations. At high polymer concentrations, this competition forces both weakly and strongly charged polymers to anchor onto the membrane in the brush-like conformation, thereby sequestering smaller PIP2 clusters. The PS lipids cluster around the polymer/PIP2 complexes when the amount of tetravalent PIP2 lipids is insufficient to neutralize the anchored cationic polymers. We also observe that the monolayer can be overcharged due to the anchoring of polymers at high polymer concentrations. Our work thus approaches an improved understanding of the anchoring processes from a fundamental perspective based on the estimates of the stability and the structural variations of the polymers/monolayer complex with important molecular factors. (C) 2016 Elsevier Ltd. All rights reserved.