|I'm usually dubious about posters who claim that their cat is a Maine Coon (officially, you can only be a Maine Coon if you have pedigree papers!), but at least you say "part" Maine Coon. And I tend to agree. We go to lots of cat shows and have seen HUNDREDS of Maine Coons in the past year, and you have a definite Maine Coon look about you, although your body shape (as seen in the picture of you on top of the kitchen cabinet) also suggests plain old domestic longhair heritage. For starters, let's talk about probability. Maine Coons are the indigenous cat of Maine and nearby areas (including Canada), and so it's only natural that there are a lot of mixed breed cats in those areas who show clear Maine Coon characteristics (after all, the Maine Coon was just a moggy before it became a pedigreed cat!). Norwegian Forest Cats are closely related to Maine Coons, and some theorize that they may be a Maine Coon ancestor, but I do not think you look as much like a Norwegian Forest Cat as a Maine Coon, nor is it as likely, probability-wise, that you would have NFC blood in you, as they are much less common than MCs (ditto Ragdoll--you are NOT Ragdoll, I can almost guarantee that).
Anyway, you have the following characteristics that look to us like evidence of Maine Coon heritage: The long, very fluffy tail (Norwegian Forest Cats tend to have shorter tails); the concavity in the profile (hard to see in the photo, however); the "britches" (thick fur on the back of the legs); the rich red tabby color (same as me!); and the very sweet, nicely-set, slightly almond-shaped eyes--which are typical of the older, more traditional breed standard. I'm not sure about your ears--in some photographs they look like those of a typical domestic longhair, and in some, they look like those of the older breed standard Maine Coon (the newer look, favored by TICA--The International Cat Association--calls for very tall, upright ears with exaggerated lynx tufts). Norwegian Forest Cats tend to have ears that are smaller than those of MCs and DLHs. Your tabby markings are those of the classic, or blotched, tabby, rather than the striped markings of the mackerel tabby. Although blotched tabby markings are common in pedigreed American shorthairs (whose ancestors are American domestic shorthairs), personally I've never seen an American mixed breed cat with blotched/classic tabby markings; they're always striped (think of your garden variety grey tabby). But pedigreed Maine Coons with the tabby pattern, including red tabbies, most commonly have the blotched pattern (circles/whorls on the side). You can see a typical version of these markings on my page. I'm not sure about what kind of markings the original, indigenous, non-pedigreed Maine Coons had, though. As for the mane around your neck (or lack of it)--true, Norwegian Forest Cats typically have this mane, but some Maine Coon cats do, too, and some don't. Actually, there's a big variety in fur length and fur type among Maine Coons; there are some with rather shortish hair (see my sister Leila), but always with a bushy tail. As for the fur matting, I have to disagree with the poster who says that MC fur is always prone to matting. (I can't say about NFCs, however.) In our Maine Coon family, we have very silky fur that gets greasy between baths, but does NOT mat. We have Maine Coon friends who mat easily and have coarser hair, but recently I was praised at a cat show by the judge for my silky (but shaggy!) fur, which makes me think that silky fur is actually a trait that meets the breed standard more than coarser, easily matted hair.
You're a big boy of a size typical of MCs (I'm a bit on the small size), and the fact that you're still growing is also typical of MCs, who mature slowly (some say it takes up to three years to reach maturity). (Just make sure not to get too fat! "Big" and "fat" are two different things!)
Oh, and I'm not sure what you mean about a "big nose," but Maine Coons are distinguished by a very prominent, square muzzle (mine's a bit small).
In conclusion, I would say that not only is there a strong likelihood of your having a Maine Coon ancestor (probably in the very recent past, too), but that cat may very well have been a pedigreed cat, and not some Maine Coon wannabe. Again, it's hard to tell just from your photos, but that's my conclusion. And I very rarely tell cats that they look like they really are part Maine Coon.
Although I don't think you're purebred, it bears repeating that, compared with some other breeds, there is quite a large variation in looks among Maine Coons, regarding general size, fur length, facial features (eyes, ear size and ear setting), noseline, muzzle, the presence/absence of a mane, fur quality, and tail length/fluffiness.
Anyway, you ARE a gorgeous cat, and my Meowmy, who loves red tabbies, would have scooped you up for her own if she'd found you before your human did!