Zero ATK Fighting zero ATK
Looking at the rules nothing happens:


  0 ATK monsters
  
  Monsters with 0 ATK cannot destroy anything by battle. If two Attack Position monsters with 0 ATK battle each other, neither monster is destroyed.


End of page 46 (or PDF page 50) here: https://img.yugioh-card.com/uk/rulebook/Rulebook_v9_en.pdf