Low-dimensional magnetoelectric (ME) materials are attracting high attention both from the scientific and technological communities due to their interesting electrical, optical and mechanical properties allied to their novel applications in micro and nano smart-devices, drug delivery platforms, heterogeneous catalysis, tissue engineering, biosensors and bio-actuators, among others. Once the low dimensionality of these materials complicate the direct measurement of their performance at a large range of magnetic fields and high filler contents, this work theoretically evaluates low dimensional ME structures from spherical to ellipsoidal and fibre-shaped. The structures are based on CoFe2O4/poly(vinylidene fluoride) composites and the simulations are performed through the finite element method (FEM). Results for 50 wt percentage (wt.%) CoFe2O4 content samples reveal ME coefficients of 182 V/cm at 684 Oe for the spheres and 4241 V/cm at a magnetic field of 208 Oe on the medium eccentricity (of 1200) ellipsoidal structure. These fibre shaped ellipsoids exhibit higher ME values than the spheres and the axisymmetric fibres: 1601 V/cm at 30 Oe for an ellipsoid with eccentricity of 3200. Further, the fibrilar structure strongly decreases the ME performance and operational magnetic field to 14.7 V/cm at 1.38 Oe. These results establish the potential and limits, in terms of magnetic field and electric response, of the use of these composites and structures on technological ME device applications. Further, it demonstrates that suitable tuning of shape and dimensions allow to strongly increase ME response of the composites.