The saturation adsorbed amount of polymers on solid surfaces is mostly found to be independent of the polymer transport rate, or flux J, to the surface. In most cases this is because the experimental rate of transport strongly deviates from the relaxation rate in the polymer layer. We studied the adsorption of savinase on SiO2 from aqueous solution and found that the transport rate is an important parameter in the adsorption kinetics. The adsorption process can be viewed as an attachment to, followed by spreading of a polymer molecule over the surface. In this way the adsorbed amount strongly depends on J if the time for transport to the surface is in the same range as the spreading time. Using an analytical "growing disk" model for the polymer adsorption, we are able to, at least qualitatively, describe the adsorption kinetics.