I find it interesting at how far many of his successors went to distancing themselves from Caesar while still trying to remain close to him... if you see what I mean.

Antony wanted to take over the position of Caesar but to gain the popularity of the people and Senate he abolished the dictatorship, yet he still had to present himself as the heir to Caesar to the soldiers. Even Octavian, who happily portrayed himself as the son of the divine Julius to gain popularity, something which Lepidus quickly learned in Sicily, would later claim to the heir to the powers of Pompey, the great defender of the Republic, when he was shrouding his autocratic power in the dismembered remains of the 'public thing'

Of course this all highlights the ambiguity of the times and of politics in general