The importance of cell surfaces in the self-assembly of proteins is widely accepted. One biologically significant event is the assembly of amyloidogenic proteins into aggregates, which leads to neurodegenerative disorders like Alzheimer's and Parkinson's diseases. The interaction of amyloidogenic proteins with cellular membranes appears to dramatically facilitate the aggregation process. Recent findings indicate that, in the presence of surfaces, aggregation occurs at physiologically low concentrations, suggesting that interaction with surfaces plays a critical role in the disease-prone aggregation process. However, the molecular mechanisms behind the on-surface aggregation process remain unclear. Here, we provide a theoretical model that offers a molecular explanation. According to this model, monomers transiently immobilized to surfaces increase the local monomer protein concentration and thus work as nuclei to dramatically accelerate the entire aggregation process. This physical-chemical theory was verified by experimental studies, using mica surfaces, to examine the aggregation kinetics of amyloidogenic alpha-synuclein protein and non-amyloidogenic cytosine deaminase APOBEC3G.