What breed of pig are these pigs?

They are probably pot bellied pigs. They mature at about 150 pounds if not overweight, which is quite small compared to a farm pig. They will grow until 3-5 years of age.  Some do keep them in their homes and yards, but they are best kept in barns with access to a pasture area. Unless you live in a tropical climate, they do need access to either indoors or a heated shed or barn for cold weather. 

Some people do think they make good pets, and maybe for some people they do. But they certainly have drawbacks. I've known a few people personally who got a pot bellied pig as a pet. I know no one who got another after the first was gone. Pigs are very smart, but not particularly biddable, which can make them challenging behaviorally. They're quite sturdy and muscular, so you'll find attempts to try to make them do anything they don't want to do are likely to fail, and also be met with an extremely loud squealing/screaming noise. They're often pretty affectionate with their owners, but many can be aggressive towards other pets as well as unfamiliar people. They can be litter trained, but their waste smells very foul. Certainly not something I would want in my house, or my yard. They tend to be very destructive to yards, as they do have the instinct to root and wallow. You can say goodbye to having a nice garden or lawn unless you have a separate securely fenced area for the pig.