Summary: An adjacent vertex distinguishing (AVD-)total coloring of a simple graph \(G\) is a proper total coloring of \(G\) such that for any pair of adjacent vertices \(u\) and \(v\), we have \(C(u)\neq C(v)\), where \(C(u)\) is the set of colors given to vertex \(u\) and the edges incident to \(u\) for \(u\in V(G)\). The AVD-total chromatic number, \( \chi^{\prime\prime}_a(G)\), of a graph \(G\) is the minimum number of colors required for an AVD-total coloring of \(G\). The AVD-total coloring conjecture states that for any graph \(G\) with maximum degree \(\Delta\), \(\chi^{\prime\prime} _a(G)\leq\Delta+3\). The total coloring conjecture states that for any graph \(G\) with maximum degree \(\Delta\), \(\chi^{\prime\prime} (G)\leq \Delta+2\), where \(\chi{\prime\prime} (G)\) is the total chromatic number of \(G\), that is, the minimum number of colors needed for a proper total coloring of \(G\). A graph \(G\) is said to be AVD-total colorable (total colorable) graph, if \(G\) satisfies the AVD-total coloring conjecture (total coloring conjecture). In this paper, we prove that for any AVD-total colorable graph \(G\) and any total-colorable graph \(H\) with \(\Delta(H)\leq \Delta(G)\), the corona product \(G\circ H\) of \(G\) and \(H\) satisfies the AVD-total coloring conjecture. We also prove that the graph \(G\circ K_n\) admits an AVD-total coloring using \((\Delta(G\circ K_n)+p)\) colors, if there is an AVD-total coloring of graph \(G\) using \((\Delta(G)+p)\) colors, where \(p\in \{1,2,3\}\). Furthermore, given a total colorable graph \(G\) and positive integer \(r\) and \(p\) where \(1\leq p\leq 3\), we classify the corona graphs \(G^{(r)}=G\circ G\circ \cdots \circ G (r+1 \mbox{ times} )\) such that \(\chi_a^{\prime\prime} (G^{(r)})=\Delta(G^{(r)})+p\).