They like them cuse they are easy to hold with their paws, being the football shape! Even my big girls love them! They will fetch them on command! The pups are still learning. We have found the medium size the best, all around size for all our girls. 
@planetsaver said in Basenji for me or not ?:
Will be a problem to leave him alone, let's say 10 days / month an average of 9 hours a day.
Also I do not want to have to much trouble with the neighbours, but I understand he can make some noise sometimes, maybe he can be trained to stay alone and not to bark that much.
Why would you even think about training a hunting hound to stay home alone ? I would never let my Basenjis alone for more than 4 hours, and even that is very rare. 3 hours is absolute maximum.
Like @tanza, I have sold puppies into apartment environments as long as all other boxes ticked positive. Someone there all the time, proper attention to training, not just leaving the dog alone, especially not as a puppy.
btw, he won't bark at all. As you would know if you had really researched the breed. He will cry and scream but not bark !
No. At least you are asking questions but I really think you should find another breed.
