In this paper we prove existence of nonnegative solutions to parabolic Cauchy–Dirichlet problems with (eventually) singular superlinear gradient terms. The model equation is ut-Δpu=g(u)|∇u|q+h(u)f(t,x)in(0,T)×Ω,\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} u_t - \Delta _pu=g(u)|\nabla u|^q+h(u)f(t,x)\qquad \text {in }(0,T)\times \Omega , \end{aligned}$$\end{document}where Ω\documentclass[12pt]{minimal}
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\begin{document}$$\Omega $$\end{document} is an open bounded subset of RN\documentclass[12pt]{minimal}
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\begin{document}$${{\,\mathrm{{\mathbb {R}}}\,}}^N$$\end{document} with N>2\documentclass[12pt]{minimal}
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\begin{document}$$N>2$$\end{document}, 0<T<+∞\documentclass[12pt]{minimal}
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\begin{document}$$0<T<+\infty $$\end{document}, 1<p<N\documentclass[12pt]{minimal}
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\begin{document}$$1<p<N$$\end{document}, and q<p\documentclass[12pt]{minimal}
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\begin{document}$$q<p$$\end{document} is superlinear. The functions g,h\documentclass[12pt]{minimal}
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\begin{document}$$g,\,h$$\end{document} are continuous and possibly satisfying g(0)=+∞\documentclass[12pt]{minimal}
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\begin{document}$$g(0) = +\infty $$\end{document} and/or h(0)=+∞\documentclass[12pt]{minimal}
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\begin{document}$$h(0)= +\infty $$\end{document}, with different rates. Finally, f is nonnegative and it belongs to a suitable Lebesgue space. We investigate the relation among the superlinear threshold of q, the regularity of the initial datum and the forcing term, and the decay rates of g,h\documentclass[12pt]{minimal}
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\begin{document}$$g,\,h$$\end{document} at infinity.
