I would like to describe in some way an asymptitoc behaviour of solutions to Cauchy problems for degenerate parabolic equations with p-Laplacian and gradient absorption term in generalized Baouendi-Grushin type settings. Among qualitative properties under the consideration will be existence, Holder continuity and some sharp estimates of radii of the supports of the solutions and essential maximums of solutions. Also the criterion for the mass decay fenomenon will be discussed.