The combination of a neodymium borohydride, Nd(BH4)3(THF)3 (1) or Cp*Nd(BH4)2(THF)x (2), with MgnBuEt (BEM), affords an efficient and highly selective (up to 96.7% 1,4-trans) catalyst for butadiene polymerization. In the presence of excesses of Mg co-catalyst, polymer chain transfer takes place between neodymium and magnesium, and significant amounts of 1,2-units are observed. When considered for butadiene-styrene statistical copolymerization, the catalytic system based on 2 showed a good ability to produce poly[(1,4-trans-butadiene)-co-styrene)], with strong impact of the Mg/Nd ratio on the yield and on the copolymer microstructure, including the percentage of inserted styrene (up to 16.9 mol%). Whatever the co-monomers concentration the polybutadiene backbone remained 1,4-trans. The precise microstructure of the polymers and copolymers was thoroughly analyzed by means of high resolution NMR spectroscopy (900 MHz) and MALDI-ToF spectrometry.