  Motivated by recent scanning tunneling microscope (STM) experiments on cobalt
clusters adsorbed on single wall metallic nanotubes [Odom {\em et al.}, Science
{\bf 290}, 1549 (2000)], we study theoretically the size dependence of STM
spectra and spin-flip scattering of electrons from finite size ferromagnetic
clusters adsorbed on metallic surfaces. We study two models of nanometer size
ferromagnets: (i) An itinerant model with delocalized s, p and d electrons and
(ii) a local moment model with both localized d-level spins and delocalized
cluster electrons. The effective exchange coupling between the spin of the
cluster and the conduction electrons of the metallic substrate depends on the
specific details of the single particle density of states on the cluster. The
calculated Kondo coupling is inversely proportional to the total spin of the
ferromagnetic cluster in both models and thus the Kondo temperature is rapidly
suppressed as the size of the cluster increases. Mesoscopic fluctuations in the
charging energies and magnetization of nanoclusters can lead to large
fluctuations in the Kondo temperatures and a very asymmetric voltage dependence
of the STM spectra. We compare our results to the experiments.
