Adsorption of fully hydrolyzed polyvinylamine on cellulose fibers in the short term was investigated by supplying the polymer to the fibers, first instantaneously by pouring the polymer solution into a jar containing the fiber dispersion (jar experiments) and second, at controlled rates (the reactor experiments). In the latter case, the rate of supply of polymer to the fiber dispersion confined in the reactor was monitored by setting the concentration of the solution being injected at a controlled rate. The concentration of the polymer solution exerts a paramount influence on the kinetics of adsorption and on the amount of polymer adsorbed at (or near) fiber surface saturation, while the rate of polymer supply only plays a minor role. The main observation is the emergence of two types of polymer layers corresponding to diffuse and dense layers. The former were characterized by adsorption layers of density smaller than 0.65 mg/g cellulose that are composed of adsorbed polymers having sustained extended flattening in the adsorbed state. The latter reach densities as high as 10 mg/g cellulose when the fiber surface is fully coated, thus indicating that reconformation is limited or even impeded at short terms. The threshold adsorption corresponds more or less to equilibrated layers, since the final coverage determined at adsorption equilibrium did not exceed 0.6 to 0.7 mg/g cellulose.