Well, the stallions can be approved by numerous breed associations if they pass the stallion licensing tests. My filly's sire is an Oldenburg because he was born in that region in Germany, even though his sire and dam are Holsteiners. Her sire, Coromino, is approved German Oldenburg and also NA/WPN (Dutch), SWANA (Swedish) and 2 other associations (don't recognize their logo on his webpage). He was presented to the inspectors and they must have felt that he was nice enough to license for their association to add outside bloodlines.
Same with mares - lots of TB mares seem to be approved in the GOV as well as other warmblood mares whose owners want to breed them to an Oldenburg stallion and register the offspring as an Oldenburg. I've seen a few Arab mares approved as well.
Inspections happen the year the horse is born (or when they're a yearling if you have a vet's note saying they were too sick/injured to be presented the year before). The inspectors evaluate the conformation and then the foal is turned loose and the mare is led around the arena at the trot. Ideally the foal should trot along her side so the movement can be evaluated - but that doesn't always happen ;) Then the inspectors "convene" and decide whether or not to give the foal premium status (just a "hey, this is one of the nicer foals here", not really anything super special - the horse isn't crap if it's not given premium). If it's not premium, it's just registered. If it is, then it's registered and given a little "premium plaque". They then take a few mane hairs for DNA testing and draw markings on the papers like they do for coggins. After all of that's done, the inspectors will speak about each foal's weaknesses/strengths and their reasoning for awarding/not awarding premium and/or stallion prospect/foal of distinction awards. Then you pay for registration, get the foal's microchip and go home :) A few weeks later you'll get their passport in the mail. Atleast that's how it works for GOV.
Mare inspections for non-Oldenburgs also happen at foal inspections - they're the pretty much the same. Evaluate confo, walk and trot and decide what book they're going to be placed in.
Here’s a summary of the different mare books and their requirements:
Main Mare Book – at least 4 generations of only approved stallions in the mare’s pedigree. Only Main Mare Book mares can produce stallion candidate sons, and only foals out of Main Mare Book mares are eligible for Premium Foal awards at inspection.
Mare Book – at least 3 generations of only approved stallions in the pedigree.
Pre-Mare Book I – at least 2 generations of only approved stallions in the pedigree.
Pre-Mare Book II – less than 2 generations of only approved stallions in the pedigree.
And I found this:
Also, when we say a mare must have at least 4 generations of only approved stallions in her pedigree to qualify for Main Mare Book, we mean that EVERY stallion in the past 4 generations must have been in one of these three categories: 1) a Warmblood stallion that was formally and officially licensed for breeding by an approved registry; 2) a TB stallion registered with Jockey Club or its counterpart in another nation; 3) a purebred Arabian stallion or an Anglo-Arab (Arabian / TB) stallion registered with Arabian Horse Registry or International Arabian Horse Association, or their counterparts in another nation. Non-licensed WB stallions and stallions with QH, Paint, Appaloosa, Saddlebred, TWH, Morgan, Standardbred, pony, or draft horse blood are NOT acceptable within a 4 generation pedigree.
Hope it helps :)