The Kennel clubs of the countries where the dog originates, makes the decision which will be accepted as an individual breed. The designer dogs of today are in line to become the new breeds added onto the lists of purebred dogs. How they go about issuing 'papers' or pedigrees is another matter. That is probably why it takes so long for a new breed to be accepted into the club. Mixed breed dogs tend to be healthier, because they are not as susceptible to diseases passed on as a result of inbreeding.
