We extend, in many variables, results established by Cegrell [2] on the continuation of the plurisubharmonic functions defined outside closed subsets, of open sets of $\mathbb{C}^n$, having zero Ronkin [6] gamma capacity. This will be achieved by the continuation of some plurisubharmonic functions, having on ``a priori" growth, through some thin (meaning to be precised) closed subsets of $\mathbb{C}^n$ ($n\geq 1$).