tioned parenthesis (which does not vanish) by certain Keldysh diagrammatic approximations [19]. Recent studies often employ the GW approximation [5–10]. Results obtained within the GW approximation are certainly of interest [5–8], although limitations and artefacts are also significant [9, 10]. Methodologically, the weak point of this approach is the fact that its physical content is hard to understand. Thus, it is difficult to assess a priori its validity for a real case. The attempt to benchmark the GW approximation against exact results for transport led to ambiguous conclusions [9, 10]. Within this framework, both important effects (i. e., intramolecular correlations and molecule-electrode coupling) are treated in an approximate manner. Consequently, it is difficult to conclude which of them is better or worse approximated. It makes more sense to benchmark the GW approximation for those isolated extended molecules, wherein electron correlations play an important role, and which are also employed in transport experiments. Recent studies in this direction are significant, but only considered atoms and very small molecules so far [33, 34]. In Introduction, we mentioned that the results for transport should be partition inde- pendent. Obviously, within the present approach, where correlations in distant parts of electrodes are neglected, the partition independence means and is demonstrated by the fact that, by making the extended molecule larger than a certain size L$_{c}$ , the results do not (notable) change. Regarding the size-(in)dependence of the results of other approaches to correlated molecular transport, attention should be paid to the following important aspect. The fact that calculations accounting approximately for electron correlations (like DFT’s or GW’s) yield results that saturate with increasing N , does not necessarily imply that they are physically meaningful. The saturation could be a mathematical artefact, because such approximative methods become poorer at larger sizes and cannot reliably describe subtle correlations basically localized within the molecule in a system including larger and larger parts of uncorrelated electrodes. Correlation effects at larger sizes are likely underestimated, and this renders a correlated system resembling more an uncorrelated one, wherein the size- dependence is absent (cf. Sect. I), and hence the aforementioned saturation. On the contrary, if molecular correlations can be accounted for by means of an accurate Green’s function G r i of an isolated and sufficiently large extended molecule, size-independent results can be trusted: they indicate that correlations are negligible at the interfaces between electrodes and the extended molecule. The present numerical results indicate that the extended molecules to be employed for 20