In the novel, The Call of the Wild, what is Judge Miller's relationship with Buck?

Judge Miller was Buck’s first owner.  He lived in a big house in Santa Clara Valley, California.  Buck,

“….ruled the estate. Here he was born, and here he had lived the four years of his life" (London 6).

The judge had house dogs and kennel dogs, but Buck ran the whole place. 

“...[Buck] was king, -- king over all creeping, crawling, flying things of Judge Miller's place, humans included" (London 6).

Buck was very close...

Judge Miller was Buck’s first owner.  He lived in a big house in Santa Clara Valley, California.  Buck,

“….ruled the estate. Here he was born, and here he had lived the four years of his life" (London 6).

The judge had house dogs and kennel dogs, but Buck ran the whole place. 

“...[Buck] was king, -- king over all creeping, crawling, flying things of Judge Miller's place, humans included" (London 6).

Buck was very close to the family.  He would swim and hunt with the boys, take long walks with the girls, and keep the Judge company by the library fire.

The gold rush in Alaska had increased the demand for large dogs capable of pulling dog sleds. Buck was a large dog, one hundred and forty pounds, and he would make an excellent sled dog.  The Judge’s greedy gardener, Manuel,  recognized that fact and decided to kidnap the dog and sell him.

The day Buck disappeared, the Judge was at a meeting, and the boys were at a club. Manuel took Buck out for an evening walk. He took Buck to a train station where he met a man who paid him $100 for the dog. After a train ride, Buck was taken to a small saloon. His brass collar was cut off. Without that collar, no one would know that he belonged to the Judge. That night, when the shed door rattled, Buck would expect to see the faces of either the Judge or the boys, but no one came to his rescue.  He would never see the Judge again.