Adsorption of randomly branched polyelectrolytes, "hairy" particles and internally structured macromolecules, collectively denoted as heterogeneously charged nanoparticles, on charged surfaces is important in many technological and natural processes. In this paper, we will focus on (1) the charge regulation of both the nanoparticle and the surface and (2) the surface complexation between the particle functional groups and the surface sites and will theoretically study the adsorption using the extended surface complexation approach. The model explicitly considers the electrochemical potential of a nanoparticle with an average (smeared-out) structure and charge both in bulk solution and on the surface to obtain the equilibrium adsorption. The chemical heterogeneity of the particle is described by a distribution of the protonation constant. Detailed analysis of the chemical potential of the adsorbed nanoparticle reveals that the pH and salt dependence of the adsorption can be largely explained by the balance between an energy gain resulting from the particle and surface charge regulation and the surface complexation and an energy loss from the unfavorable interparticle electrostatic repulsion close to the surface. This conclusion is also supported by the strong impacts that the chemical heterogeneity of the particle functional groups, the magnitude of the surface complexation, the number of the functional groups, and the size of the particle have on the adsorption.