Who's your daddy? Equine Paternity Rights

It is a surprisingly frequent inquiry that I receive: if a stallion impregnates another owner's mare without permission- would the stallion's owner have any claim of right to the resulting foal?

The question reminds me of the equine romantic epic, King of the Wind by Marguerite Henry.  The author weaves a fiction (though based on true characters/ horses) that the prized grey mare Lady Roxana was to be bred to the European stud Hobgoblin, but she rejected his breeding attempts; the Godolphin Arabian stallion then deliberately broke loose and bred with her (creating uproar and scandal).  
The resulting foal was Lath, who reached legendary status for his speed.

So would the Godolphin Arabian's owner have rights to Lath or his earnings, even though the impregnation was without the consent of Lady Roxana's owner?
Horses are property and are not legally treated as children, so a "paternity right" would not necessarily arise. 
The mare owner would likely have a cause of action (could sue) the stallion's owner for trespass to chattel (chattel is personal property) and for damages to her mare.  
These damages could include: the lost opportunity to breed the mare to a more profitable stallion, or if the mare was not to be bred, then the wear and tear on her body of gestation and delivery, in addition to any calculable physical harm the mare might have suffered in the live cover.
If the mare is used in a breeding business and the impregnation interferes with a contractual breeding, damages could include tortious third-party interference with a contractual/ economic relations.

However, if I were in the shoes of the stallion's owner, and my stallion has a high stud fee (let's just say a $1 million fee to breed with my stallion), then perhaps I could have a claim for unjust enrichment and request restitution (essentially, reimbursement) from the mare's owner of any detriment I have suffered, or of a reasonable amount of the undeserved gain by the mare's owner.

The arguments would of course be dependent on the specific facts of the case.  Furthermore,
public policy generally doesn't want people to profit from their crimes (though criminals do profit from their book sales sometimes!), so if the stallion's owner had acted illegally or tortiously, public policy would likely discourage his or her ability to profit and dictate that the owner should not be entitled to an economic interest from the stallion's trespassory cover.

It is an interesting concept to consider- thanks to my readers for suggesting the topic!