  An adjacent vertex distinguishing total $k$-coloring $f$ of a graph $G$ is a
proper total $k$-coloring of $G$ such that no pair of adjacent vertices has the
same color sets, where the color set at a vertex $v$, $C^G_f(v)$, is $\{f(v)\}
\cup \{f(vu)|u \in V (G), vu \in E(G)\}$. In 2005 Zhang et al. posted the
conjecture (AVDTCC) that every simple graph $G$ has adjacent vertex
distinguishing total $(\Delta(G)+3)$-coloring. In this paper we confirm the
conjecture for many coronas, in particular for generalized, simple and
$l$-coronas of graphs, not relating the results to particular graph classes.
