I give up. I have a group of five real life friends that i got into the game and our wee little alliance can’t regularly take down a 3* titan. I am going to hunt for a new home for us. At what level titan do you start getting a regular chance at 4* AM? We all seem to be kicking around with a couple of 5* heros and way too many 4* twiddling their thumbs, stuck at 3/60.
Hey sorry to hear that, good luck finding a good alliance that can kill titans regularly 
I would offer you a spot on mine but we don’t have room for 5.
To answer your question, what increases with higher star titans is the amount of ascension materials you get per titan. The higher the stars, the more rolls you get. Supposedly the odds of better stuff increases too, I don’t doubt this to be true, however I don’t have proof of that.
However, more loot rolls = more chances at rare materials, so that alone is worth killing high rarity titans.
The amount of rolls is determined by the loot tier you get, and the loot tier is determined by the stars of the titan + your damage rank.
So using the above information, what that means is that killing a 3* titan in 1st place gets you A+ grade. Adding that together – 3+ 3 = loot tier 6, which nets you 2 ascension material rolls for loot.
See below for how many rolls you get on higher loot tiers.
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For two or three months I was playing in alliance of my own (just me and my daughter) We were killing 1-3* Titans. I didn’t get any single unfarmable item.
After that I went back to the alliance that hunts 7-9* Titans. There I started getting unfarmable materials once in three killed titans.
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4* mats are rare at any level, you can kill many titans without getting any.
3* mats become much more abundant as you get to 8* and above.
Just to clarify, 4* mats are the ones used to final ascend 5* heroes. 3* mats are for 4* heroes. I know this causes a lot of confusion.
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Thank you for clarifying!
Most of my mats come from titans, but A+ on 8* doesn’t guarantee ascension mats 
had that too often, today was another day without…
But of course there’s a better chance. Good luck with finding a new home!
Better one to show would be this one Dave
Got some preliminary results for the liklihood of getting ascension mats at each loot tier
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