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We study the self-similar solutions of the equation \[ u_{t}-div(| \nabla u|^{p-2}\nabla u)=0, \] in $\mathbb{R}^{N},$ when $p>2.$ We make a complete studyof the existence and possible uniqueness of solutions of the form \[u(x,t)=(\pm t)^{-\alpha/\beta}w((\pm t)^{-1/\beta}| x|) \] of any sign, regularor singular at $x=0.$ Among them we find solutions with an expanding compactsupport or a shrinking hole (for $t>0),$ or a spreading compact support or afocussing hole (for $t<0).$ When $t<0,$ we show the existence of positivesolutions oscillating around the particular solution $U(x,t)=C_{N,p}(| x|^{p}/(-t))^{1/(p-2)}.$

Self-similar solutions of the p-Laplace heat equation: the case when p>2