In this talk, we consider parabolic equations in divergence form that only satisfy an ellipticity property for values of the gradient lying outside the unit ball. As usual, these equations are investigated in a space-time cylinder that is taken over a bounded spatial domain for some finite time T>0. The vector field present in the diffusion term of the equation is given as the gradient of some non-negative function F that depends on the space-time variable (x,t) and also on the gradient Du(x,t) of the solution. For the function F we assume: F is only smooth for gradient values outside the unit ball but vanishes entirely within the unit ball. The last property justifies the denotation "widely degenerate". Moreover, the regularity of F may break down on the unit sphere. Additionally, we allow a right-hand side f in the equation that is only required to belong to a certain Lebesgue space. As our main result, we establish that for any weak solution u, the composition K(Du) is continuous within the domain for any continuous function K that vanishes in the unit ball.