How will i know that a shih tzu is not a full breed?

The only qway to know for sure is if the dog is from a reputable breeder and has a legitimate Kennel Club resgitration certificate (AKC).
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Just because a dog is purebred does not mean it is a good specimen.
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Not necessarily. Put up a picture. You can also tell us about the breeder or pet store you probably got them from. Pet Stores are all bad. http://stoppuppymills.org/ http://prisonersofgreed.org/

You can also google Back Yard Breeders, Puppy Farms, etc.

AKC doesn't mean it's a good breeder. Many breeders with AKC registered puppies are crappy at best. In fact, most of them are crappy. If you want a reputable Shih Tzu breeder, find one on this site. http://www.americanshihtzuclub.org/

Many people won't go with AKC, but would rather go with UKC.

Edit: Don't know why the TD. AKC will register puppy mill puppies, and allow them to breed. Don't know if UKC will or not.

Here's a horrible breeder that's full of shyte about the HSUS. They say they don't operate a single shelter. Well, where I live they do. http://www.hoffmanstoys.com/

But it's the fact that they breed such poor quality Poodles that makes them so horrible. Not what they say about the HSUS. And their puppies are sold AKC. There are THOUSANDS of others JUST LIKE THEM.

Here's another horrible breeder that sells AKC puppies. They make mutts. No good breeder would ever make mutts. http://www.suespoos.com/

Both of these are puppy mill operations.
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A real pure breed dog would come with certifications from his kennel or breeder. I hope you would love this dog regardless of his pedigree or lack of.
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If the parents are AKC then you have a full bred dog if you bought the dog from a BYB then no telling.
You can tell by the features. Yes a professional breeder can tell if it is pure breed, or just a poorly bred dog
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Ask the breeders here: http://www.pets4you.com/shihtzu.html
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