I have been designated “Straight Dope Curator of Critters” and “Straight Dope Curator of All That Walks, Crawls, or Flaps” by Cecil himself, which is all you need to know. 
I don’t know about pedigree, but when they revamped the Paris subway, crossing big rodents about forearm length (nose to hind) was not rare. They do not have the same shape as cats, but their bodies were longer than my n° 12 shoe. Whatever their origin, they were big, and snouting out the best fast food cans they could find
I, personally have seen, up close, an Asian Paddie Rat, that was as large as a small cat. I was in Indonesia, on the island of Bali, at a guesthouse, on a rice paddie, not far from the black beaches of Singaraja. It ran through our room. We both saw it.
I know. Not evidence. Still, I saw it with my own eyes.
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I don’t know about pedigree, but when they revamped the Paris subway, crossing big rodents about forearm length (nose to hind) was not rare. They do not have the same shape as cats, but their bodies were longer than my n° 12 shoe. Whatever their origin, they were big, and snouting out the best fast food cans they could find
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What do you mean, exactly, by an “Asian Paddie Rat”? A Rattus rat, or something else?
Because if you mean a Rattus rat, then what you saw was very unlikely to have been actually the size of a small cat, no matter what you think you saw. If you caught and measured that rat, I’m confident it would be much smaller than your mental estimate of its size.
It probably won’t make any difference to say this once again, but size is very difficult to estimate in the wild, especially for an untrained observer. A lot of bird field identification depends on making size judgments, and I know from experience that estimates can vary due to many circumstances. I’ve been told about plenty of eagles that turned out to be small hawks, and albatrosses that were ordinary gulls.
Anecdotes about “I saw some big rats once” like the ones above are of no value with regard to actually answering the OP.
I realize I won’t convince you.
We owned a small black cat, we’d left back home in care of a friend. We immediately looked at each other, and, in unison, said, “Did you see that? That’s bigger than our cat!”
Paddy Rats are what everyone I asked, called the kind of rats they had. They were very fat, and cleaner than city rats, and well fed from living in the rice paddies, as I understood it. And I didn’t see it in the wild, it was in our room, next to a waste basket, actually.
Again, I recognize, not evidence, not going to convince you, just reporting what I actually saw with my own eyes. Anyone may choose to believe or discount my report, obviously!
Like I said, if it was a Rattus, you probably just misjudged the size. You may have thought it was as large as your cat, but without a direct comparison that estimate could have been off.
Nutria are more like beavers, really. They aren’t like giant rats at all. (In my opinion, I didn’t google up the latin names. They look like beavers and in my experience are very aquatic and not very scary.)
And I really do think most of the ‘rats as big as cats’ that people believe they’ve seen were possums. Or Opossums if you want to be fancy.
Those things skeer the HELL out of me. I’ve seen them back down large dogs. From my limited involvement with Rattus, they tend to run down to the rathole. Possums seem like they’d fight you just for the thrill of it.
They’re kinda the methaddicted rodent teenagers of your nightmares.
I hate possums. There is no functional ecological niche they fill that could not be filled by a raccoon. The raccoon does everything the possum does, while also not looking and smelling like hell spawn.
Likely he means the Rice-field Rat, Rattus argentiventer, which if anything is smaller than Rattus N.
Since the OP didn’t rule out Shel Silverstein:
And I’ll take Colibri’s word that no specimen of R. rattus or R. norwegicus that large has ever been documented, but Wikipedia says that there are 64 different species in genus Rattus. Is one of the other 62 possibly that large?
Walker’s Mammals of the World, the standard reference on mammals, indicates that Rattus norvegicus is among the largest species in the genus, with “most other species being considerably smaller.” If there was a species that was dramatically larger - especially any that was anywhere near the size of a cat - I would expect them to mention it. (One Google result indicates that norvegicus is the largest member in the genus, but I am not able to access the article itself.)
At any rate, R. norvegicus is certainly the largest commensal species of Rattus, and is also undoubtedly the species being referred to when people talk about “rats the size of cats.” Such observations, per the best available information, appear to be due to mis-estimates based on inaccurate visual observations, hoaxes, or exaggerations.
Exaggeration? Nonsense! Cryptozoobeasts do exist! Here’s a spideresque horror the size of a rat. It kills camels! A whole pack!
The size of a kitten, maybe.
That said, once while out running after a downpour, I saw some animal swimming along a flooded drainage ditch that at first glance I thought was a woodchuck – it was only a few hundred feet farther on that it clicked in my mind I’d also seen a long skinny tail. So I don’t know. Maybe it was a possum. Didn’t look like one, though.
Of course this is in jest, but I would note that the photo makes the “camel spiders” look larger than they actually are.
As mentioned in several posts upthread, the coypu or nutria is introduced in many states in the US and looks something like an aquatic woodchuck with a long tail. The native muskrat is much smaller but is larger than a Rattus rat.
Another:
Which may or may not count since he’s genetically altered. Which brings up an interesting question, is he a new species post-alteration? Or would he have to procreate and the offspring would be the new species?
Any one individual cannot constitute a “new species.” “Species” is defined on a population basis, that is a population that has restricted or no gene flow with another naturally-occurring populations in nature. Since Master Splinter cannot be said to “occur in nature,” he would not qualify even if there were a Splinterette somewhere about.
I’ll tell you this - the rats I saw in S.E. DC a few years ago creeped me right the hell out. I got that massive adrenaline burst you get when something just absolutely does not fit into your accepted definition of the world. (I was inside the car so in no danger.) While I accept that adrenaline may have affected my memory, these were bigger than the photos of the R.N. above.
After asking around I concluded that they must have been Norway rats, but looking at the linked photos has me wondering. Their noses were more pointy, but their eyes were not bulgy, and their tails were shorter than normal rats. (At the time I thought their tails were shortened from fighting, but this fits R.N. too.) They were hunched up fighting and eating, but even so the bodies were rounder than R.R. Still elongated, but not slender. Their ears were on the flatter side, not “Mickey Mouse ears.” I am from Virginia and know an Opossum (even a baby one) when I see it. That’s not what I saw either.
Colibri - any chance that these were R.N. x R.R. hybrids? Sometimes hybrids produce giants don’t they?
What I saw would definitely not compare to “large squirrel” they were more cat-sized. It was also Winter and very cold, so there may have been some fur fluffage affecting my size estimate.
Another question: Does size = weight in this case? Equal weights of Pomeranian v. Bulldog give you completely different sizes, afterall. What is the relative torso length to a 2# rat v. a 3# cat? The cat certainly has more leg height than a rat, how much weight does that take up?
Makes sense. So Splinter would just be a failed mutation of rattus rattus? That is, unless he finds Splinterette and they start making baby rattus splinterus’ (splinteri? splinteruses?).
Bah, I’m sure there are plenty of rats around that are as big as turtles. That image doesn’t prove anything.