We provide the solution for optimizing the power and resource allocation over block-fading relay-assisted broadcast channels in order to maximize the long term average achievable rates region of the users. The problem formulation assumes regenerative (repetition coding) decode-and-forward (DF) relaying strategy, long-term average total transmitted power constraint, orthogonal multiplexing of the users messages within the channel blocks, possibility to use a direct transmission (DT) mode from the base station to the user terminal directly or a relaying (DF) transmission mode, and partial channel state information. We show that our optimization problem can be transformed into an equivalent "no-relaying" broadcast channel optimization problem with each actual user substituted by two virtual users having different channel qualities and multiplexing weights. The proposed power and resource allocation strategies are expressed in closed-form that can be applied practically in centralized relay-assisted wireless networks. Furthermore, we show by numerical examples that our scheme enlarges the achievable rates region significantly.