Sam Simon -- Beloved Dog Coping with Death

Sam Simon's cherished 3-year-old dog is heartsick over his owner's death, but there's already a new owner who is doing everything he can to ease the blow.

Tyson Kilmer, one of Sam's close friends who is also a dog trainer, tells us shortly after Sam was diagnosed, he called with a request -- love and cherish his Italian mastiff after he died.

Tyson gladly obliged, especially because of his history with Columbo. He trained the pooch for aggression issues when he was a pup.

Tyson had a plan he put into motion months before Sam died. Columbo spent time at Tyson's home so the permanent move wouldn't be too jarring.

We're told Columbo is adjusting well, but misses his dad. Kilmer took one of Sam's favorite hooded sweatshirts and laid it on Columbo's bed ... which the dog snuggles up with at night.

Good news ... Columbo has a girlfriend ... a pit bull named Kasha Fierce.

The biggest adjustment for Columbo ... moving from Pacific Palisades to Sherman Oaks ... woof.