In the U.S. approximately 53 percent of American dogs are crossbreeds or mongrels, and approximately 47 percent are "pure breeds".
To put it another way about 3,710,000 dogs of mixed ancestry, and approximately 3,290,000 "pure breed" dogs, are acquired every year.
Most of the "pure breeds" in the U.S. are not registered with the American Kennel Club (AKC) or anywhere else; they are simply matings of dogs that look to be purebred examples of their type.
In 2016, to pick a year, the AKC registered less that 500,000 pure bred dogs. To put it another way, AKC registrations represented about 15 percent of pure bred dogs and about 7 percent of all dogs acquired that year. Since 2006, the AKC has not, so far as I can tell, published counts by breed -- a way of hiding their collapsing registration numbers.
Assuming the same canine distribution as was evident in 2006 when breed count data was last reported, of the less than 500,000 pure bred dogs registered by the AKC in 2014, the top 10 breeds (out of 184 breeds total in 2015) represent a little over half of all dogs registered, while the bottom 50 breeds will represent less than 1.5 percent of all dogs registered.
How do these numbers compare to the UK?
Not too far off.
It's estimated there was a total of 9.4 million dogs in the U.K. in 2010. A population of 9.4 million dogs will require a replacement cohort of about 1 million dogs a year, In 2010, the U.K. Kennel Club registered a total of 216,856 purebred dogs, so U.K. Kennel Club registrations are going to total about 22 percent of all dogs in the U.S.
The 20 most popular dog breeds in the U.K. Kennel Club account for 72% of total registrations, while the rarest 100 breeds account for only 2% of registrations -- a distribution very similar to what we see in the U.S.