NO dimers adsorbed on alumina supported silver nanoparticles (Ag NPs, radii R approximately 1-6 nm) show decreasing desorption temperatures and complex behavior of photoinduced desorption with decreasing NP size. In particular, for resonant excitation of the (1,0) Mie plasmon at 3.5 eV the photoinduced desorption cross section increases with 1/R, showing a pronounced enhancement (40 times) at R approximately 2.5 nm compared to Ag(111). At 4.7 eV the translational temperature of photodesorbed NO increases strongly with 1/R. We discuss these trends and peculiarities in terms of the size-dependent properties of the Ag NPs.