Biomaterial-associated thrombosis remains a persistent challenge whenever medical devices are inserted in blood vessels. The issue is principally addressed by the development of antithrombogenic coatings that prevent the formation of blood clots, e.g. by limiting adsorption of fibrin - the core protein network of a clot. Charged polymers (i.e. polyelectrolytes and zwitterionic polymers) show potential as coating materials for medical devices, and we here investigate these polymer coatings in the context of biomaterial-associated thrombosis. Our findings indicate that fibrin polymerization can yield a surface-dependent distribution of fractal-like branched structures and amorphous aggregates, with surface-induced fibrin formation dominating for anionic polymer interfaces and recruitment of bulk-formed fibrin dominating for cationic polymer interfaces. In addition, we identify coatings containing zwitterionic sulfobetaine groups as promising candidates for antithrombogenic biomaterials.