Dust distributions at different stages during the collapse. First row: Mass dust-to-gas ratio. Second row: Number dust-to-gas ratio. Third row: Resistivities profile and ion and electron numerical densities (Hall resistivity: dotted line for the negative values and solid line for the positive ones). Dashed black lines: Reference resistivities obtained with a fixed MRN dust distribution. Fourth row: Parallel, perpendicular, and Hall conductivities, and the evolution of the peak size of the dust distribution. Comparison between different values of the grain surface energy expressed in cgs units (erg cm⁻²).