We want to analyze both regularizing effect and long, short time decay concerning a class of parabolic equations having first order superlinear terms. The model problem is the following: $$\begin{aligned} {\left\{ \begin{array}{ll} \displaystyle u_t-\text {div }(A(t,x)|\nabla u|^{p-2}\nabla u)=\gamma |\nabla u|^q &{} \text {in}\,\,(0,T)\times \Omega ,\\ u=0 &{}\text {on}\,\,(0,T)\times \partial \Omega ,\\ u(0,x)=u_0(x) &{}\text {in}\,\, \Omega , \end{array}\right. } \end{aligned}$$ where $$\Omega $$ is an open bounded subset of $${{\,\mathrm{{{\mathbb {R}}}}\,}}^N$$ , $$N\ge 2$$ , $$0<T\le \infty $$ , $$1<p<N$$ and $$q<p$$ . We assume that A(t, x) is a coercive, bounded and measurable matrix, the growth rate q of the gradient term is superlinear but still subnatural, $$\gamma $$ is a positive constant, and the initial datum $$u_0$$ is an unbounded function belonging to a well precise Lebesgue space $$L^\sigma (\Omega )$$ for $$\sigma =\sigma (q,p,N)$$ .