If an animal broke out of the fence at night or bandits broke the fence and the animal caused damage the owner or the Shomer of the animal is Patur. (1)
The Beraisa of Rebbi Yosef states that if an animal of one of the partners of a shared courtyard or the animal of a guest damages with Shen or Regel the property of another partner or guest he is Chayav. (2)
If an animal causes damage in Reshus ha'Nizak the owner is Chayav for everything, in Reshus ha'Mazik he is Patur for everything, in a shared courtyard he is Patur for Shen and Regel. (3)
Rebbi Tarfon holds that Keren in Reshus ha'Nizak is Chayav Nezek Shalem.
If an animal damages with Shen and Regel is a Reshus that does not belong to either the Nizak or the Mazik the owner of the animal is Patur.
If an animal damages with Shen and Regel is a Reshus that is reserved only for the Nizak for produce but is reserved for both the Nazik and Nizak for oxen it is considered a Reshus ha'Nizak and the owner of the animal is Patur.
If an animal damages a Talis or a Talis damages an animal the Nizak may not take the animal or a Talis for his payment and instead the damage is evaluated and the Mazik pays the cost of the damage.
The Dinim of Ona'ah do not apply to land Shetaros and servants.
Land and servants are acquired with a Kinyan Kesef.
The Mazik may pay for damages with anything of value.
If the Nizak is collecting for his damages from the orphans of the Mazik he may only collect from Karka, however if the Nizak grabbled movable objects for his payment from the Mazik before he died he may keep it.
Only an expert Beis Din has the authority to collect a Knas but not a Beis Din of Hedyotos.
It is a Machlokes if after someone admits to a Knas witnesses testify that he is Chayav if he is Patur from the Knas.
A BIT MORE
1. However, if the animal broke out of the fence during the day the owner is Chayav because he should have made the effort to corral the animal before it caused damage.
2. It is referring to case that the shared courtyard is reserved for the use of produce but not for oxen and therefore it is regarded as a Reshus ha'Nizak for Shen and Regel.
3. It is referring to case that the shared courtyard is reserved for the use of both produce and oxen and therefore it is regarded as a Reshus ha'Rabim and Shen and Regel is Patur in a Reshus ha'Rabim
COLLECTING FROM METALTELIN
If the Nizak is collecting for his damages from the orphans of the Mazik he may only collect from Karka. The Rif says that now that the Rabanan have decreed that a Chov may be collected from Metaltelin of the orphans a Nizak may also collect from the Metaltelin of the orphans. However, Rabeinu Efrayim disagrees and he says that the decree only applies to a Ba'al Chov so that the door will not be close on potential borrowers but Nezikin is something that is unusual and the decree of the Rabanan does not apply to Nezikin. The Rosh says that nowadays Metaltelin has the same Din as Karka even without the decree of the Rabanan because people rely on Metaltelin in the same way that in the past people relied on Karka.
If the courtyard was reserved for both of them for oxen and for the one for other things and he brought his Talis into the courtyard and the ox of the other partner damaged his Talis and the Talis also damaged the ox the damages are not offsetting and the two damages are evaluated and whichever one was damaged more receives compensation for the difference between the two damages. (Shulchan Aruch CM389:17)