It is found that 4,4'-bipyridines functionalized in their 3,3'-positions with Frechet dendrons of 0th to 3rd generation self-assemble with (dppp)M(II) triflates (dppp: bis-(diphenylphosphino)propane; M=Pd, Pt) into metallo-supramolecular squares. They bear a nanometer-sized cavity inside an unpolar dendritic shell. A total of eight amide groups decorate the rims of the cavity connecting the dendrons to the square. Evidence for their formation up to the third generation comes from ESI-FTICR mass spectrometry and NMR experiments. Based on these results, the presence of significant amounts of other polygons or open-chain oligomers can be excluded. Exchange processes have been studied by variable-temperature NMR spectroscopy and by following the ligand exchanges between different squares by mass spectrometry. The ligand exchange is much slower for the Pt(H) squares as compared to their Pd(II) analogs. Visualization of films of these dendrimers using atomic force microscopy (AFM) provides information on their molecular dimensions. After deposition of a square monolayer on the surface, a slow reorganization within this layer is observed which leads to the formation of "tower-like" aggregates and multi-layer formation. The interplay of interactions between the dendrimers and the surface and interactions between different dendrimers are invoked to rationalize the observations.