dna test ?
check it for characteristics ?
hair sample ?
how do they find out if a cat is a certain breed ?
so there is a group of people tracking every breed of cat in the world ??
This is my furry kid Satina. I am almost positive that she is part Bengal Kitty & possibly Egyptian Mau. I saw your post and was wondering what your thoughts were on what her breeding might be, maybe I am correct in my guess? She is super intelligent, way more then any other kitty I have had as a companion, knows what she likes and how to get it, is uber affectionate, LOVES to play catch and 'fetch' with her little catnip mice and loves the water. She is so different from any of my other furry kids, we are so blessed to have her as a companion!
Looks like a lovely non-pedigree to me. All good cat slaves recognise how special their own owners are and you are clearly very well trained!
Remember that all pedigrees are descended ultimately from non-pedigrees, so just about everything in pedigree cats can be seen in non-pedigrees. Some things are seen a lot - classic and mackeral tabby patterns - others only in the area the breeds originated in, or where an entire pedigree has slipped out and impregnated the local females. For example if a Siamese male gives his owner the slip, his offspring will have normal patterns but Siamese patterns will pop up in his grandchildren by the various unneutered local females. However whilst they have the siamese pattern (and possibly the voice!) they are NOT siamese cats. Just moggies with Siamese in their background.
Not only do the registries record pedigrees and outline breed standards (what the cat should look like), they also have breeding policies. The GCCF (main registry in the UK) has a web page listing the breeds they register, the description and the registration policies. It also has links to the number of cats registered by breed.
Asothers have said, pedigrees are tracked by a number of registries, and not just for cats and dogs. Race horse pedigrees are available online and go right back to the origins of the breed in the UK - to the original foundation stallions. There are stud books for breeds of cattle and sheep (and goats and other domestic animals I imagine), some going back to the late 1700s which is very soon after Robert Bakewell started systemic selective breeding of domestic livestock to improve them. AFAIK some of the UK Breed studbooks are among the oldest for cattle and sheep - horse pedigrees (for example) in some parts of the world go much further back.
It's also worth pointing out that the two breeds you suggest as possible origins, the Mau is a very rare cat in the UK - only 194 Maus were registered in 2010. The Bengal is less rare, but still numerically well behind the most popular breeds.