steady-state current does depend or not on the position in the extended molecule of the cross-sectional area through which it flows [7, 13–15]. To summarize, a reliable approach of the transport in correlated molecular systems should not only yield a steady-state current that does not depend on the transverse areas at . . . L 3 , L 2 , L 1 , M, R 1 , R 2 , R 3 , . . . , but also on the way in which the extended molecule is delimited by the various rectangles, as schematically depicted in Fig. 1. The remaining part of the paper is organized in the following manner. In Sect. II, we present the theoretical framework, and in Sect. III the rationale for the concept of a suf- ficiently large extended molecule. The interacting resonant level model, which is used in all numerical calculations of this paper, is described in Sect. IV. Next, in Sect. V we re- port numerical results for the linear conductance. The case of narrower band electrodes is examined in Sect. V A, Sect. V B is devoted to the case of wider band electrodes. To be specific, for these two cases we shall use the terms organic and metallic electrodes, respec- tively. In Sect. VI, we present a simple renormalization scheme, which works surprisingly well and yields results that exhibit a very weak size dependence even for unrealistically strong Coulomb contact interactions. In Sect. VII, we discuss the relevance of numerical results for realistic systems, and in Sect. VIII we present the conclusions. FIG. 1: Schematic representation of a typical two-terminal setup for molecular transport. A molecule M is linked to two left L and right R electrodes. In a correct approach, the steady-state current is site-independent and does not depend on the way in which the total system is partitioned into the central part (extended molecule) and the electrodes. In the figure, the different partitions are depicted by the dashed-line frames. t$_{L}$ t$_{R}$ L R L R L$_{8}$ L$_{5}$ L$_{4}$ L$_{3}$ L$_{2}$ L$_{1}$ M R$_{1}$ R$_{2}$ R$_{3}$ R$_{4}$ R$_{5}$ R$_{8}$ 3