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Recent transport experiments in vertical double quantum dots (DQDs) show that Pauli exclusion principle plays an important role [1, 2] in current rectification. In particular, spin blockade (SB) is observed at certain regions of dc voltages, and the interplay between Coulomb and SB can be used to block the current in one direction of bias while allowing it to flow in the opposite one. Then DQDs could behave as externally controllable spin-Coulomb rectifiers with potential application in spintronics as spin memories and transistors. Spin de-coherence and relaxation processes [3, 4] induced by spin—orbit (SO) scattering [5] or hyperfine (HF) interaction [6], have shown to reduce SB producing a leakage current in the voltage region where the blockade occurs. We theoretically analyze recent experiments of transport through two weakly coupled vertical QDs [1]. In these experiments current flow is allowed when the electrons in each QD have antiparallel spins and a finite gate voltage allows one electron in the left dot to tunnel sequentially to the right one. However, there is a similar probability for the electron coming from the left lead to be parallel or antiparallel to the electron spin occupying the right dot. In the first case, the electron cannot tunnel to the right dot due to Pauli exclusion principle and SB takes place, presenting a plateau in the I/Vdc curve. [ABSTRACT FROM AUTHOR] more...