Co-doped ZnO powder oxides show magnetic behavior with combination of (i) antiferromagnetic pairs formed by two nearest-neighbor Co2+ ions and (ii) magnetic clusters originating from the parallel magnetic interaction between isolated Co2+ ions. We report that a high number of parameters can act on the magnetic cluster sizes, such as cobalt-ion and charge-carrier concentrations (depending on the atmosphere and temperature of the synthesis, co-doping with A3+ metals, etc.) or oxide morphology (large grain/nanopowder). A ferromagnetic signal is not achieved because the magnetic clusters are spatially limited and/or because they involve a low number of Co2+ ions. This observation pointed out here as a key parameter is also supported by virtual supercell simulations. Thus, we propose that the reached global as-super-paramagnetic behavior is on one hand due to the grain surface that limits the charge carriers' mean free path and on the other hand to antiferromagnetic pairs acting as blocking barriers. The disparities of the results found in the literature may be due to variation of the concentration and the efficiency of the blocking barriers (possibility of the charge carriers to jump or not jump these barriers).Read less <