We discuss some fundamental aspects of the pure-geometrical models related to the connection between the scattering amplitude of composite hadrons and the scattering amplitude of the constituents partons in the multiple diffraction theory. A comparative study of the parton-parton amplitudes currently used in these models is presented, showing its main mathematical and physical features and also a comparison with results from a model-independent analysis, for the dynamical part of the eikonal.48520072018