What role does a protein's size have on protein-protein interactions?
Protein interactions occur mostly (if not all) through residues that are on the "surface" and exposed to the milieu in which they exist, be it cytoplasmic or extracellular. So, a naive thought would be to guess that a greater surface area means a greater swathe of exposed regions and probable interacting parts. One protein can bind many others, even simultaneously, through different such interaction surfaces. However, other factors also determine whether a given set of two proteins interact, most important being where they localize in a given cell. If one protein is nuclear but the other on the plasma membrane, it is highly unlikely that they ever interact even if thermodynamics highly favors complex formation. Interaction between two proteins also depends on their respective conformations, which can further be regulated by events such as post translational modifications (eg., phosphorylation by a kinase), bound nucleotide state (eg., GTP vs GDP in a G protein). Last, scaffolds can also sequester and organize protein clusters together spatially and increase the probability of them interacting. All put together, I think it is highly unlikely that just looking at 3D surface area of a protein will say much about its "interactability" with other proteins.