The relaxation of electronic spins S of paramagnetic species is studied by the field-dependence of the longitudinal, transverse, and longitudinal in the rotating frame relaxation rates R-1, R-2, and R-1p of nuclear spins I carried by dissolved probe solutes. The method rests on the model-independent low-frequency dispersions of the outer-sphere (OS) paramagnetic relaxation enhancement (PRE) of these rates due to the three-dimensional relative diffusion of the complex with respect to the probe solute. We propose simple analytical formulas to calculate these enhancements in terms of the relative diffusion coefficient D, the longitudinal electronic relaxation time T-18, and the time integral of the time correlation function of the I-S dipolar magnetic interaction. In the domain of vanishing magnetic field, these parameters can be derived from the low-frequency dispersion of R-1 thanks to sensitivity improvements of fast field-cycling nuclear relaxometers. At medium field, we present various approaches to obtain these parameters by combining the rates R-1, R-2, and R-1P. The method is illustrated by a careful study of the proton PREs of deuterated water HOD, methanol CH3OD, and tert-butyl alcohol (CH3)(3)COD in heavy water in the presence of a recently reported nonacoordinate Gd(III) complex. The exceptionnally slow electronic relaxation of the Gd(III) spin in this complex is confirmed and used to test the accuracy of the method through the selfconsistency of the low- and medium-field results. The study of molecular diffusion at a few nanometer scale and of the electronic spin relaxation of other complexed metal ions is discussed.