Political Situation after Caesar dies a natural death?

Julius Caesar surving the Ides of March is populat enough among the AH community, but most of the discussion focuses on what he would do, how he’d fare against the Dacians and Parthians, etc.

So, here’s our parameters: Caesar avoids assassination (either the plot is foiled or it falls apart on its own). He goes on campaign and conquers Dacia, and take Mesopotamia from Parthia (likely through client kings). He then returns to Rome and dies peacefully in his bed in, say 34 BC, just to give us a nice round number.

What does the political situation look like, both during the rest of his life and after? Would we still see a civil war after his death? Would he have favored one potential successor enough to make the transition to post-Caesar Rome relatively smooth?
 
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