The successor inherited nothing de jure. It was up to the Senate to grant him the same powers as his predecessor. What became common practice was that the current ruler would groom his successor, including him in the government and having him take bigger responsibilities. He would thus be granted offices by the Senate with the current ruler's recommendation. Eventually, upon the current ruler's death, the successor would have everything necessary to rule on his own. The best example of this practice in the early empire is the Augustus-Tiberius transition. The reason this transition was much more peaceful than the following was because of the efforts to ensure ability and familiarity with the new rulers. In fact, this specific practice is also one of the reasons why the Good Emperors suffered no overt problems while transitioning.