Depositing cationic polyelectrolytes (PEs) from micellar solutions that include surfactants (SU) onto surfaces is a rich, complex, highly relevant, and challenging topic that covers a broad field of practical applications (e.g., from industrial to personal care). The role of the molecular architecture of the constituents of the PEs are often overruled, or at least and either, underestimated in regard to the surface properties. In this work, we aim to evaluate the effect of a model biomimetic surface that shares the key characteristics of the extreme surface of hair and its concomitant chemo- and physisorbed properties onto the deposition of a complex PEs:SU system. To tackle out the effect of the molecular architecture of the PEs, we consider (i) a purely linear and hydrophilic PE (P100) and (ii) a PE with lateral amphiphilic chains (PegPE). Using numerical self-consistent field calculations, we show that the architecture of the constituents interfere with the surface properties in a nonintuitive way such that, depending on the amphiphilicity and hydrophilicity of the PEs and the hydrophobicity of the surface, a re-entrant adsorbing transition can be observed, the lipid coverage of the model hair surface being the unique control parameter. Such a behavior is rationalized by the anticooperative associative properties of the coacervate micelles in solution, which is also controlled by the architecture of the PEs and SU. We now expect that PEs adsorption, as a rule, is governed by the molecular details of the species in solution as well as the surface specificities. We emphasize that molecular realistic modeling is essential to rationalize and optimize the adsorption process of, for example, polymer conditioning agents in water-rinsed cosmetic or textile applications.