Context. Both theory and observations of star-forming clouds require the simulations which combine the co-evolving chemistry, magneto-hydrodynamics and radiative transfer in protostellar collapse simulation. A detailed knowledge of self-consistent chemical evolution for the main charge carriers (both gas species and dust grains) allows to correctly estimate the rate and nature of magnetic dissipation in the collapsing core. Last is of crucial importance for answering the grand question of star and planet formation: the magnitude and spatial distribution of magnetic flux as the initial condition to protoplanetary disk evolution. Aims. We use a chemo-dynamical version of RAMSES, described in a companion publication, to follow the chemo-dynamical evolution of collapsing dense cores with the various dust properties and interpret the occuring differences in the magnetic diffusivity terms. Later are of crucial importance for the circumstellar disk formation. Methods. We perform 3D chemo-dynamical simulations of 1 M⊙ isolated dense core collapse for a range in the dust size assumptions. The number density of dust and it's mean size are affecting the efficiency of charge capturing and the formation of ices. The radiative hydrodynamics and dynamical evolution of chemical abundances are used to reconstruct the magnetic diffusivity terms for clouds with various magnetisation. Results. The simulations are performed for a mean dust size ranging from 0.017µm to 1µm, and we adopt both a fixed dust size and a dust size distribution. The chemical abundances for this range of dust sizes are produced by RAMSES and serve as an input to calculations of Ohmic, ambipolar and Hall diffusivity terms. Ohmic resistivity only play a role at the late stage of the collapse, in the innermost region of the cloud where gas density exceeds few times 10 13 cm −3 . Ambipolar diffusion is a dominant magnetic diffusivity term in cases where mean dust size is a typical ISM value or larger. We demonstrate that the assumption of a fixed 'dominant ion' mass can lead to one order of magnitude mismatch in the ambipolar diffusion magnitude. 'Negative' Hall effect is dominant during the collapse in case of small dust, i.e. for the mean dust size of 0.02 µm and smaller, the effect which we connect to the dominance of negatively charged grains. We find that the Hall effect reverses its sign for mean dust size of 0.1µm and smaller. The phenomenon of the sign reversal is strongly depending on the number of negatively charged dust relative to the ions, and quality of coupling of the last to the magnetic fields. We have adopted different strength of magnetic fields, β = Pgas/Pmag = 2, 5, 25. We observe that the variation on the field strength only shifts the Hall effect reversal along the radius of the collapsing cloud, but do not prevent it. Conclusions. The dust grain mean size appears to be the parameter with the strongest impact on the magnitude of the magnetic diffusivity, dividing the collapsing clouds in Hall-dominated and ambipolar-dominated cloud...