I personally am very careful about a horse's ancestors when I am looking at breeding. I don't mind 5 or 6 generations back having a couple of common ancestors, but close line breeding, or in breeding, definitely not. I had a thoroughbred, bred for racing, with almost no line breeding in her closer relatives. Once you got back to the 1800's you started to see repeat names, but she was fairly out crossed, and a very nice example of a racing thoroughbred. My Arabian mare I had was the same way, she had three names, each only repeated twice in the fifth generation, but most of her lines were all different names, and again, a very nice example of the Arab breed. That being said, I do see a point in further generations back of having some common names, because they do set a type, and especially if the breed has gone off in an unforseen direction, sometimes recrossing to something you know can bring it back. I know someone who had an Arabian, decided to breed her to one of the stallions from the farm where she was originally bred, and somehow when the breeder sent them the semen for ai, they sent the wrong stallion, and she ended up getting bred back to her dad. They had no idea until the baby was born with several different problems, and a color he shouldn't have been if his sire was the horse they asked for. He has basically spent his life as an expensive pasture pet, and the owner opted to not breed her mare to the right stallion. There are risks associated with line and in breeding, and I agree that unless you really know what you are doing, have done extensive research on those lines, and on any potential problems that have arisen, you should stick with not doing it.