the purifior

principle

A horse is a purebred (or thoroughbred, only one breed in his origins)
or a crossbred (more than one breed in his origins).

You can see the breed of a horse looking at his origins chart >

Here you can see 4 hanoverians horses, but only one is a thoroughbred, because he has 100% hanoverian breed.

If your horse is a crossbred, and you want to have a purebred horse, you can purify him if you breed him with a purebred horse, and then breed the foal with the purebred horse again, during several generations, and you get a purebred foal at the end

how many generations to purify a horse

It depends on the start % of the breed you want to obtain as pure and unique breed for your last foal.
For each generation, we can calculate the % of breeds in the foal's origins.
When a breed has less than 1%, it disappears from the origins chart.