The incoherently coupled soliton families are predicted in photovoltaic photorefractive crystals illuminated by E-polarized incoherent uniform back-ground irradiation with a divider resistance under steady-state conditions. These soliton families can be established provided that the incident optical beams share the same polarization and wavelength, and are mutually incoherent. When these incoherent coupled soliton families propagate together, all components can propagate stably in photorefractive crystal. Moreover, such soliton families reduce into spatial soliton or incoherently coupled soliton pairs when they contain only one or two components. The 14 kinds of incoherently coupled spatial soliton families can be obtained from this theory by adjusting the value of the divider resistance, E-polarized back-ground irradiation, the biased electric field and photovoltaic electric field. Previous theories advanced individually elsewhere for these soliton families can be obtained by simplifying this theory under appropriate conditions.