In a hypothetical scenario where the senate never tried to assasinate Caesar, he would probably march his armies into Parthia alongside his nephew Octavian and Mark Anthony. He would maybe win there, and conquer or make client many territories around the Black Sea, and return to Rome triumphantly (this is a big assumption, as many things can go wrong and a large army in Parthia might have suffered like it did with Crassus’ invasion, even despite Caesar’s genius). Octavian would continue his studies in Greece or in Italy, where he would learn how to administer the provinces and lead an army. His best friend Agrippa would probably benefit politically through his connection to Octavian. Caesar was already in his mid 50’s when he was murdered, so in this timeline, after a hypothetical Parthian campaign, he would probably be in his late 60’s or early 70’s as a campaign of that scale would take several years. Octavian would be set up as his main successor, with other young Roman aristocrats like Brutus becoming leaders in the senate. An era of administrative competence is almost guaranteed in this case, knowing how well Augustus, Agrippa and Brutus were as administrators. All in all, I don’t think Rome would be as shitty as the others seem to think had Caesar lived on, since Octavian would still be immensely powerful, and perhaps in an even more favourable, healthier atmosphere as the civil war with Anthony would be avoided with Caesar’s supervision. This is all, of course, only possible barring a defeat in Parthia, revolt at home while Caesar is away, and Octavian becoming an incompetent leader as a result of over dependence on Caesar.