What are the different methods and their respective odds of getting/earning character specific items?

I've just started playing Final Fantasy Record Keeper and managed to unlock Aerith, along with earning Cloud, Kain, and a few other early characters. I know that all of these characters have rare items that are specific to them, such as the Buster Sword for Cloud. So far, I've only seen people mention receiving these items from the rare item relic pulls.

What are the different ways of earning character-specific items? Are there any conditions before being eligible (like perhaps unlocking a character before their item is available)? Are the odds of each method known if they are, what are those odds?