There is an interesting tshuvah of R’ Tzvi Pesach Frank (in Har Tzvi) on a Chanukah issue where, while both the questioner and the response fail to mention it, without knowledge of a Ketzos I think you will largely miss the point (maybe they just assumed you would make the connection because once upon a time, as Havolim once wrote, the Ketzos was the bread and butter of every lamdan.) I’m going to break this post into chunks to make it easier to digest (I hope!).
The owner of an animal that stomps on an object is chayav to pay back its full price in damages. However, if instead of touching the object directly, the animal kicks a stone at the object and breaks it, the owner pays only half; this is the unique din of tzeroros.
The gemara (B.K. 17b) discusses the case of an object dropped off the roof of a building which is then smashed by someone else on its way down: Do we look at the object as already broken once it left the roof – basar m’ikara azlinan – or do we say that it’s not broken yet, and the one who smashes it pays? Rava raises the question; Rabba opines that we treat the object as already broken.
What if an arrow is shot at the object, and before it hits its target, someone else smashes the object? Sounds parallel to the gemara's case, but Tosfos says there is a distinction. In the gemara’s case the object itself is acted on by the party who drops it from the roof. In the case of shooting an arrow, the person firing the arrow does not act directly on the object; therefore, he is not liable; the person who smashes the object before the arrow hits is.
Tosfos proves the point: if shooting at an object is the same as acting directly on an object, then we’ve eliminated the distinction we started with between stomping on an object, which is one of the avos nezikin, and kicking a stone which later hits an object (tzeroros).
Given that there is a distinction between the cases, the question that begs asking is why. There are a number of possibile explanations, but I’ll keep it simple and put it this way: relative to the person who takes a swing at the object on the way down, the person who already acted directly on the object in a way that would destroy it bears greater liability. But relative to the person who has only indirectly acted on the object by shooting an arrow at it, the person who acts directly on the object by taking a swing at it is more liable.
The Ketzos (390:1) suggests that some Rishonim may not agree with Tosfos, and in part II I'll give you his proof and then tie that in to R' Tzvi Pesach Frank on Chanukah bl"n. Stay tuned.