All dictators who come to power are charismatic statesmen with a keen political sense. They construct cult followers and develop relationships with underlings who gladly keep them in power. Their authoritarian administration sees to it by overseeing multiple human rights abuses, both at home and abroad.
Children who take over a dictatorship rarely have the same qualities as their parent. They do have the cult followers because it was developed for them long ago. Those who worked for the parent, and who still have their positions, realize that everything they own will be lost if the new dictator goes under. Charisma and keen political sense is no longer a requirement for their new dictator in training. In fact, these qualities are often sorely lacking.
The only dictator in waiting that I can think of who did possess the qualities mentioned above was Saif Gaddafi of Libya. Of course, we can say that he does not fit the mold because he never had the chance to follow in his father’s footsteps. Unfortunately for him, he was too wrapped up in his fathers legacy. Another way to put it is; he rolled the dice and he lost.