Had a long ass answer that I erased bc what constitutes as shipping is complicated to answer for me, and I wasn't sure who you wanted to know about. Anyways, here's my list for Dami. If you want to know abt a specific character or anything in more detail, just lmk.

Damian:
1. Dickdami [everything revolves around them 2 me. even other pairings.]
2.*Timdami
3. Talondami [switches out with random pairings, depending on my mood. like injustice!Clarkdami, for example]
4. Other
5. Non-incest ships

Brudami is like. On a different plane for me, where it's between shipping, and narrative interest. Not quite sure how to explain this, but the way I engage with it feels different than like, Dickdami or Timdami. But, if it had to be on the list it'd be somewhere in the top 3.

This isn't getting into notps for him, which...I have a a lot, that I shall not name. But in general not rlly interested in anything not incestuous 4 him. he is BUILT for incest. i've said this on my priv, but i do think it's funny that writers seem to recognize that, but miss the mark in the way it's executed. a lack of a certain je ne sais quoi, and intensity that u get with ships that target dami's elektra complex and brother complex.

P.S. as much as I talk about al Ghuls and their carnal desire for each other, but I don't actually ship them all tg, except for Talia and her sister. Again, narrative interest more than anything. If anything, I'd actually say Talia/Dami is a notp for me.