This genre was inspired by Star Battle (hence the "battle" in the name).
Indeed, its main rule can be seen as generalising the 1-star-per-region rule to multiple star types: the traditional star matches the "crowned rook" piece (king + rook) - which cannot see another in the same row or column, nor in any vertex.sharing tile.
2022-06-25 Thanks to 5381 for making some puzzles and finding a bug with the cross markers, to Arvi Teikari (Hempuli) for suggesting an improvement to the rule pictures, to Karoo for finding non-uniquenesses, and to everyone else at the Thinky Puzzles server for feedback, in particular Icely who made this fun banner: 2023-06-22 Style changes: non-attacked squares are now highlighted (instead of attacking squares). Thanks to Mitchell Clarke (DireKrow) for noticing a critical bug, now fixed. 2024-01-16justkirb found a non-uniqueness in one of the puzzles (fixed) and an interesting bug 2024-06-12Icely made a video using an older version of the interface (thanks justkirb for sharing). Cross aux marks enabled and mini piece aux marks restored - thanks PinkHoodie (and Yakaki)! Original small-square highlighting restored. Genre name origin clarified and puzzles split by author. 2024-06-15puzzlettersPinkHoodie sent 1 classic - thank you!