This work focuses on adsorption of polyions onto oppositely charged surfaces and on responses to the addition of a simple monovalent salt as well as to the polyion length (degree of polymerization). We also discuss possible mechanisms underlying observed differences, of the adsorbed amount on silica surfaces at high pH, between seemingly similar polyions. This involves theoretical modeling, utilizing classical polymer density functional theory (DFT). We furthermore investigate how long- and short-chain versions of the polymer adsorb onto carboxymethylated cellulose, carrying a high negative charge. Interestingly enough, comparing results obtained for the two different surfaces, we observe an opposite qualitative response for the molecular weight. The large polymer adsorbs more strongly at a silica surface, but for cellulose at low salt levels, there are indications that the trend is opposite. Another difference is the very slow adsorption process observed for cellulose, particularly with short polymers; in fact, with short polymers, we were sometimes unable to establish any adsorption plateau at all. We speculate that the slow dynamics is due to a gradual diffusion of short polymers into the cellulose matrix. This phenomenon could also explain why short-chain polymers seem to adsorb more strongly than long-chain ones, at low salt concentrations, provided that the latter then are too large to enter the cellulose pores. Cellulose swelling at high salt concentrations might diminish these differences, leading to more similar adsorbed amounts or even a lower adsorption for short chains.