Csak hogy legyen választék... Ahogy Judith válaszánál is jeleztem, véleményem szerint az említett "bértartás", "tenyésztés", "nemesítés", "tartás" tevékenységek. A stable (istálló) főnév maga a létesítmény, ahol az említett tevékenységeket folytatják, és egy létesítmény szerintem nem lehet cél (aim), csak a tevékenység. A lovak tartása itt az USA-ban egyszerűen BOARDING. Bértartás talán lehetne "contracted boarding" vagy "boarding services", abból kiindulva, hogy az ilyen bértartás mindig szolgáltatási szerződés alapján történik, aminek neve "(horse) boarding contract".

Néhány példa:

"There are MANY laws that will help you to secure your rights, BUT you need a well written boarding contract to allow you to enforce them! Written boarding contracts for enforcement are defined by the Statute of Frauds, that has been adopted in most states and incorporated in the Uniform Commercial Code. ...
Contracts must clearly state the expectations of the owner of the facility as to the terms agreed upon. Without written agreements between you and your boarders, you may end up responsible for a hefty veterinary bill that a boarder to pay, absorbing unpaid board bills with no legal recourse, or you might face lawsuits arising from a variety of situations. A valid contract creates legal obligations between the parties, and allows for enforcement in court if the contract is broken. PUT IT IN WRITING, and oral contract leaves much up to memory which fades with time, the advantage of a written contract is that neither the existence of the contract nor its terms are in doubt."
http://www.gaitedhorses.net/boarding.htm

Horse Boarding Contract:
"The parties named above agree that "Horse Owner" (hereafter "Owner") desires Stable to provide boarding services described below, and that Stable agrees to do so under the terms described below."
http://www.printablecontracts.com/Horse_Boarding_Contract.ph...

Sample Horse Boarding Contract
"These sample forms are provided courtesy of The Bay Area Equestrian Network as an outline to follow when formulating your own documents for horse property use and boarding issues."
http://www.stablewise.com/forms.htm

Our aim is to provide very high standard livery stables beside our other ambition to breed Hungarian breeds (Nóniusz....) to exeptionally high guality...

shannonleighstables.com/
en.wikipedia.org/wiki/Livery_yard
www.cowleyhillivery.co.uk/

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Note added at 9 hrs (2011-11-20 21:36:00 GMT)
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Ezek sajátságos kifejezések, pl.
bértartásban tartani a lovat - angolul: keeping a horse at livery.

Keeping A Horse At Livery
www.equine-world.co.uk/horses_care/horse_livery.htm..discou...
At Ayrshire Equitation we understand the importance of having your horse at livery in a place where you can be sure they will receive the best possible care. www.ayrequestrian.co.uk/livery.html
There are different regulations for horses kept at livery, and those kept privately...
Providing livery from £86 per week...
www.robertsequestrian.co.uk
...discount to clients who have more than one horse at livery
...should they decide to put their horse at livery
...per week for each animal to be kept at livery