A diagnosis of adsorption on solid electrodes using semi-integral voltammetry, initially proposed by Bowling and McCreery for a reversible charge transfer without coupled chemical reactions, is re-examined in the general case. Towards this aim, we show that an asymptotic analysis of the semi-integrated (or convolved) voltammograms is sufficient to conclude. A straightforward approach is designed which enables an examination of all previous hypotheses available in the literature : reversible or irreversible charge transfer, involvement of adsorbed reactants and/or products of the charge transfer or pure diffusion, and occurrence of coupled chemical reactions. We apply our asymptotic approach to all these cases, and show that the adsorption hypothesis is the only one to yield peak-shaped semi-integrated voltammograms, while monotonically increasing S-shaped semi-integrated voltammograms are obtained in the pure diffusion approximation. We find that the exclusive assumption of adsorption versus pure diffusion is sufficient to lead to discriminating behaviour, as the consideration of all other hypotheses (reversibility of the charge transfer, coupled chemical reactions) does not alter the conclusions. Thus, a hierarchy in the various hypotheses exists, which alludes to the systematic use of semi-integral voltammetry as a practical route to the diagnosis of the involvement of adsorption phenomena in electrochemical processes. Possible restrictions to this proposal are examined, as well as the way in which they may be overcome.