When we sell muskrats on the global market, are they typically using pretty much the entire pelt, or just a portion of the pelt?

The whole rat Is being used. Backs are used for coats and bellies In most cases end up as liners In coats.

Similar situation with other furbearer species?

Not sure about all species but I'm betting that furrier Is using every bit of that fur.

I bet even a scrap or two is going for Fly Tying Material...

One by-product of the furrier made items are things like tails and faces and scraps of various sizes.

Tails from fox, coyote, Raccoon, marten all have value and can be found/bought at any black powder event.

Same thing on faces - they are usually cut off just behind the ears with maybe an inch or so of neck fur. A fox or coyote face makes a nice flap on a Buckskin pouch.

Fur scraps - fly tying. Doll making. All sorts of uses. Usually sells by the pound.

In China and Korea any of the large scraps are matched and sewn into "plates", which is like a piece of fur that works like a piece of fabric.

Very little goes to waste.

It's neat how so much of it gets put to good use.

The North American mink coat manufacturers years ago shipped all the feet and gills to Kastoria in Greece where they were made into plates for garment use.The Greeks from around Kastoria were the best fur sewers in the world.
If you have ever seen the leftover feet and gills from a mink,they are about the size of a quarter.

What are gills on a mink?

The two pieces of fur from the headskin not including the eyes or ears.

I've seen complete mink coats made from nothing but mink tails. Pretty cool looking.