This study aims to investigate the physical properties that govern polymer adsorption and desorption on chemically structured surfaces. These surfaces are considered biomimetic of natural ones that specifically exhibit a combination of hydrophobic and hydrophilic domains, like those found on hair surfaces. Understanding these processes is especially crucial when designing and developing new eco-sustainable polymers for industrial applications such as cosmetic products. In this work, we developed computational models of the hair surface and two polymers with different architectures. The first polymer studied was a semi-flexible, linear polysaccharide of natural origin, which offers potential for sustainable formulations. The second, and more complex model, was a stiff, comb-like cationic polyelectrolyte similar to petroleum-based polymers traditionally used in hair care cosmetics. We conducted coarse-grained molecular dynamics simulations to study the adsorption of the polymers onto the substrate and we found that increasing polymer concentration enhanced adsorption. The branched copolymer led to a thicker coating and exhibited a more random coverage pattern compared to the linear polymer. Furthermore, we analyzed the stability of the polymer coating by running Brownian dynamics simulations of the adsorbed polymers under a linear shear flow. These simulations revealed a correlation between flow strength and polymer desorption, thereby highlighting the importance of low desorption time for performing coatings in cosmetic applications. Despite both polymer types presenting improved resistance with longer polymer chains, the branched polymer layer exhibited higher stability. This finding demonstrates the key role of polymer architecture in assessing the coating formation, properties and performance of new eco-sustainable polymers in industrial applications.