  This work aims to study the initial-boundary value problem of the
reaction-diffusion equation $\pa_{t}u-\Delta u=f(u)+g(u(t-\tau(t,u_t)))+h(t,x)$
in a bounded domain with state-dependent delay and supercritical
nonlinearities. We establish the global existence and discuss the regularity
and dissipativity of the problem under weaker assumptions. In particular, the
existence of a global pullback attractor is proved regardless of uniqueness.
