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Our results indicate that all the heavy baryonium systems, specifically $\\Lambda_Q\\bar{\\Lambda}_Q$, $\\Xi_Q\\bar{\\Xi}_Q$, $\\Sigma_Q\\bar{\\Sigma}_Q$, $\\Xi'_Q\\bar{\\Xi}'_Q$, and $\\Omega_Q\\bar{\\Omega}_Q$ ($Q=c, b$), can form bound states. Among the heavy dibaryon systems, only the $\\Xi_Q\\Xi_Q$ system with $I=0$ and the $\\Sigma_Q\\Sigma_Q$ systems with $I=0$ and $I=1$ can exist as bound states. 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