That's an impossible question to answer. Every country and every dictator are different. Even in the Soviet Union succession was not something written in a constitution. 

Lenin in his last few weeks, advised against Stalin. He much rather saw Trotsky succeeding him. The Politburo found Trotsky a bit too revolutionary, so they elected the dull grey bureaucrat Stalin. Who was lots of things but not quite what was expected of him (dull and grey).

His highly unexpected succession was a literal Game of Thrones. Stalin was found in his bedroom paralyzed (or dead already). After the dangerous era of Stalin power was shared, with the chairman being more of a chairman and less of a Great Leader. 

Even so, old habits die hard. Leonid Brezhnev revived the Great Leader a bit, if only because of his relatively long reign. 

The USSR collapsed, and became the Russian Federation. It was never a democratic society, more like the old style nobility revived. Putin rules as an autocrat, that is how most Russian leaders rule their country. 

Elsewhere more or less the same, being no fixed pattern. Franco of course knew he was going to die. He had already groomed and prepared an heir to the throne, in his case, a real heir to the throne. His preferred choice had been murdered in a bomb attack by Basque separatist. His dead was slow and lingering. But he never foresaw that his successor changed back to democracy as soon as he could. 

It's different in every country, in every system and with every succession.