you can actually own a wolf if you get a dangerous wild animals licence however it cant live in your home as a pet, it must be in its own enclose and never taken out except to go to vets etc so no walks. Its also very expensive to meet the licence conditions and to keep it as it must be reviewed every year.
Wolf hybrids up to F3 also need a dangerous wild animals licence and have the same requirements as a full wolf. But F4 and below does not require a licence and can be kept like a pet, however they are not like dogs and most don't make good pets and with the wrong type of owner can be dangerous (not everyone is suitable to manage every breed/species)
an F4 is 4 generations away from wolf
wolf X dog = F1 -licence
F1 X dog = F2 - licence
F2 X dog = F3 - licence
F3 X dog = F4 - no licence
There are crossbreeds being bred now to look like wolfs, normally using GSD, Malamutes and Husky's. there called Northern Inuit Dogs, there is no wolf content in them some look more wolf like some don't. Many have been having hip problems due to over breeding and little health testing.
There are also two dog breeds that had wolf in its creating however that was so many years ago they are now accepted dog breeds, these are the Czechoslovakian Wolf dog and Saarloos wolf dog. Both breeds are not for novice owners both breeds should have hips tested at the least.
Many people are now crossing the above two breeds with other breeds and calling them wolfdogs but really they are not actually wolfdogs as there is no resent wolf added.
No licence is required for the Northern Inuit, Czechoslovakian Wolfdog and Saarloos wolfdog as they are dog breeds. However if you get one make sure you go to a good breeder as many are breeding them for money with the current wolfdog fad with no consideration to health and temperament.
Met a Czeh the other week, stunning dog about the same size as a GSD, the owner was surprised I knew what it was, they said it was still young and that it has been hard work. He seemed a very calm and lovely boy but from what they said they have put a lot into him and do things to work his brain rather than just an ordinary house pet.