We report on one- and two-neutron transfer reactions to study the single-particle properties of nuclei at the border of the "island of inversion". The (d,p)- and (t,p)-reactions in inverse kinematics on the neutron-rich isotope Mg-30, delivered as radioactive beam by the REX-ISOLDE facility, have been investigated. The outgoing protons have been detected and identified by a newly built array of Si detectors. The gamma-decay of excited states has been detected in coincidence by the MINIBALL array. First results for Mg-31 and from the search for the second, spherical, 0(+) state in Mg-32 are presented.