Magnetic fields can play a major role in the dynamics of outstanding explosions associated to violent events such as gamma-ray bursts and hypernovae, since they provide a natural mechanism to harness the rotational energy of the central proto-neutron star and power relativistic jets through the stellar progenitor. As the structure of such fields is quite uncertain, most numerical models of MHD-driven core-collapse supernovae consider an aligned dipole as initial magnetic field, while the field’s morphology can actually be much more complex. We present three-dimensional simulations of core-collapse supernovae with more realistic magnetic structures, such as quadrupolar fields and, for the first time, an equatorial dipolar field. Configurations other than an aligned dipole produce weaker explosions and less collimated outflows, but can at the same time be more efficient in extracting the rotational energy from the PNS. This energy is then stored in the surroundings of the PNS, rather than powering the polar jets. A significant axial dipolar component is also produced by models starting with a quadrupolar field, pointing to an effective dynamo mechanism operating in proximity of the PNS surface.