Vanquisher and Triumph

[HunGeneral]

A romani general can get this trait if he wins against and conquers teritories of the given faction - if he gets "vanquisher of Carthaginians" it means he has already won some significant battles and/or has taken some of their provinces.
Take some more from that faction and he will get the Trait "Prospective Triumphator" - this shows that he senate is thinking on giving him a triumph - you should not lead him back to rome because the senate may think he wants to take power as king.

After a few turns he will get a triat which shows that he can return to Rome for his triumph - birng him to rome and keep him there for a full turn and he will get the trait triumphator (+3 influence - corrected. Thank jhowel). I think he might get another triump aswell if he fights well against another faction - but I don't what types of "vanquisher of x" traist exist..

[jhhowell]

Triumph is +3 influence. In practice, move him towards Rome whenever you feel like it after getting the Prospective Triumphator trait. Unless it's very early in the game the travel time to Rome will be much greater than the delay time between "Prospective Triumphator" and "Triumphator". If need be you can just park him next to the city to wait it out. Or if you need to keep your general at the front, go ahead, you can claim the triumph years later if necessary.

Note, it does not seem to matter what faction you fight with a general after getting "Vanquisher of X". My most recent Triumphator was a Vanquisher of Macedonians, but became Prospective Triumphator after fighting a couple of battles against Pontus. Same thing earlier in the game with a Vanquisher of Carthaginians fighting Lusotania to earn his triumph.

A second triumph should be impossible since that would repeat a trait the character already has. One can't be "restless sleeper" twice, why should it be possible to be "celebrated triumphator" twice? And one wouldn't normally benefit from another triumph anyway, since influence is so easy to gain for Romans.