In this contribution we used solid state 35Cl (I=3/2) quadrupolar NMR to study a MgCl2/2,2-dimethyl-1,3-dimethoxypropane (DMDOMe) adduct that serves as a model system for Ziegler-Natta catalysis. Employing large Radio-Frequency (RF) field strengths we observe three spectral features with strongly varying line widths. The assignment of the spectra is complicated because of the large difference in quadrupolar interactions experienced by the different sites in the system. The satellite transitions (ST) of relatively well-defined bulk Cl sites are partially excited and may overlap with the central transition (CT) resonances of more distorted surface sites. We show that nutation NMR of the ST of I=3/2 spins yields a unique pattern that makes a clear distinction between an extensively broadened central transition and the satellite transitions of a component with a smaller quadrupolar interaction. This allows us to unambiguously unravel the spectra of the MgCl2 adduct showing that we observe CT and ST of the bulk phase of MgCl2-nanoparticles with a CQ of 4.6MHz together with the CT of surface sites displaying an average CQ of ∼10MHz.