Hello. I just discovered this forum and read quite a lot of the threads. I am gladly coming in.
One of the point to keep in mine si that, as Isabella wrote, is that roman legacies were only about privante matters as are today's legacies. The republic and the political life could be dealt only through legal acts (laws and decrees). For exemple, a law had ben passed which stipulated that Caesar's son, if he had one, would become great pontiff when his father ans current great pontiff dies.
Other important point : roman adult aristocrats probably always had a legacy in which, if they had no son through marriage they designated who would inherit their properties.*
Julius Caesar had (first ?) made Pompey the great his heir (from the marriage of his daughter Julia with Pompey in 59 BCE to the outbreak of the civil war in 49 BCE or to Pompey's death in 48 BCE).
Then, Caesar's main private heir probably was his cousin Sextus Julius Caesar. This Sextus was the great-son of annoter Sextus Julius Caesar who was consul in 91 BCE and was the brother of our Caesar's father. this younger Sextus was one of Caesar's lieutnants in the civil war and was à governor of Syria in 46 BCE when he was murdered by à seditious officer. The augustan "historiography" of course did not hint at thé part Sextus played before Octavian. It would have tarnished the legend of the predestined savior of Rome. But it is significant that in the few references to Sextus, his personnality is described in unfavourable terms.
So, if Octavius had died in 45 BCE, and if Caesar had still wanted to chose a main heir (historically, Caesar's legacy provided that Octavian inherit 75%, that his Quintus Pedius inherit 12,5% and that his other grand nephewLucius Pinarius Scarpus inherit 12,5%), it can be assumed that Caesar would have shared his inheritance between these two closest relatives. Would he have also adopted Pedius which was a lieutnant in the war of the Gauls, the same way hé did for Octavian ? Possible but not sure. And Pedius did not have Caesar's talent.
But I can not see any reason why Caesar would have adopted Anthony or Lepidus.
Firstly, Anthony was only a very distant relative of Caesar : his mother was of course a Julia, but the common ancestor between Anthony and Caesar was born not later than around 250 BCE). Besides, as far as Anthony's cousin Lucius Julius Caesar (the son of the homonymous consul of 64 BCE) is concerned, he was such an irreconcilable and cruel enemy of our Caesar (contrarily to his own father who served Caesar and worked for reconciliation) that Caesar's soldiers put him to death in 46 BCE when he was taken *prisoner.
Secondly, Caesar in fact did name neiger Anthony nor Lepidus in his legacy, whereas he named his friend (and murderer) Decimus Junius Brutus (a distant cousin of the famous Marcus Junius Brutus) as a guardian for a possible minor son of Caesar (if he had had one with Calpurnia) and as second rank heir (if Octavius, Pedius and Pinarius all died heirless). So if he did not, I don't think he would have named either Anthony or Lepidus as his heir.
So, if Octavius had died before Caesar and Caesar had still died on 44 BCE, and if either Pedius or Pinarius Scarpus or both had inherited, or even been adopted, one can imagine a situation quite similar to the one Rome knew after Sulla's death. Sulla's only son, born around 85 BCE was never a prominant political figure because he had not the talent for it. In their thirties, Caesar, Cato, Cicero, Claudius, Curio, Ahenobarbus, Cassius and others had shown their talent on the field and/or in the political arena. Not the son of Sulla.
Well, neither Pedius nor Pinarius Scarpus was a political genius.
So one can guess that Anthony would not have faced, in 44 and in the first half of 43 BCE, the absolute cynicism of Octavius who strove by all means to undermine the position of Anthony as natural political heir of the caesarian "party" by pushing very hardly for revenge over the tyrannicides and for the re-ignition of the civil war while Anthony was strugling to maintain concordia.
Without the split caused by Octavius in the caesarian party, Cicero would not have had any ground for playing one against another. Then, the caesarian party having remained united and allied to the moderates, there would probably not have been the circumstances which, in 43 BCE, drove to Anthony's being outlawed and permitted Cassius and Brutus to take control of the provinces and armies of the east by surprise.
For a few years at least, there would have been civil peace under the patronage of Anthony, the dominant figure of the republic. There would have been a competitive cooperation in the dominant caesarian-anthonian party faction. And progressively, as occured with the sullan-optimate faction in the 70's and 60's BCE, the links between the prominant leaders would have loosened. New factions would have formed inside and beyond the caesarian-anthonian coalition and ...