The SPCA said grass found in Jazz's stomach was also consistent with starvation, because a starving animal will often try to eat indigestible food.
The puppy had undergone a long period of chronic malnutrition and starvation, which would have caused prolonged distress and suffering, a veterinary pathologist found.
When examined by vets, Blacky weighed only 3.7kg, and had a six-week-old leg fracture, which would have caused a significant amount of pain and suffering.
In January, after seven weeks in the care of SPCA, Blacky weighed 9.5kg - an average weight gain of nearly 1kg per week.
SPCA Auckland chief executive Christine Kalin said the case was disturbing.
"While we're pleased to gain a conviction in this instance, it's a pity all three dogs suffered for months at the hand of the defendant and no one reported the abuse."
Katuke pleaded guilty to charges of failing to provide proper and sufficient food to animals in his care, ill-treating an animal, and failing to ensure an animal received treatment to alleviate any unreasonable or unnecessary pain or distress.
He was sentenced to 200 hours of community service, ordered to pay $997.07 reparations, and disqualified from owning animals for five years.