When did the last traces of the republic "die"?

Even though, the Republic is commonly considered to have ended with Augustus, among the general public that is. Some aspects of it did outlive Octavian.

The office of emperor being a Principate (Prince of the Republic, Primus in Parus), so still being connected to the Senate in ruling, would survive for quite a time, being slowly substituted by the Dominate, firstly fully expressed by Diocletian.

And even then, the Senate would still survive, with Constantine making a new one in Bizantium. I, personally, am do not know up until it would last in the east though.

So, is there any aspect of the Republic that managed to outlive the West?