On a surprising relation between the Marchenko-Pastur law, rectangular   and square free convolutions
  n this paper, we prove a result linking the square and the rectangular R-transforms, the consequence of which is a surprising relation between the square and rectangular versions the free additive convolutions, involving the Marchenko-Pastur law. Consequences on random matrices, on infinite divisibility and on the arithmetics of the square versions of the free additive and multiplicative convolutions are given. 
Florent Benaych-Georges (PMA, CMAP)