A systematic scanning tunnelling microscopy study of the self-assembly, intramolecular conformation and supramolecular ordering of different tetraphenylporphyrins (xTPP) with or without a central metal atom (x = 2H, Fe, Co) on Ag(111) at room temperature is presented. The investigation covers a wide range, i.e. the adsorption behaviour from the low sub-monolayer up to the multilayer regime is described in detail and conclusively discussed in regard to molecule-molecule and molecule-substrate interactions. At monolayer coverage the molecules self-assemble in domains with a square unit cell caused by "T-type" intermolecular interactions, while the orientation of the domains along the symmetry axes is determined by adsorbate-substrate interactions. Interestingly for ordered monolayers domain boundaries always separate domains of different organizational chirality but same orientation of the square unit cell. This demonstrates that in the particular system chirality obviously restricts the long range order of the supramolecular TPP assemblies. In combination with DFT calculations it is also demonstrated that the previously reported intramolecular saddle shape deformation of TPPs upon adsorption is more pronounced for metallo-TPP than for 2HTPP.