exporting artwork in Illustrator

Is your artwork is only grayscale, or do you need to convert it in grayscale before export?
The way you spell it (saying K) implies that you need to create a separation (as in creating a separation for each colour in screenprinting for example)

There are plenty of info that are missing from your post in order to truly understand your problem.
( CMYK, or spot colours if it's not grayscale before export)

In case you only want to know if you can export only a single colour without manipulating the artwork first, then the answer is no. Exporting (in PDF, JPEG, PNG and whatnot) will only export what you see, the only exception would be having the choice of wanting to include everything or only specific artboards.

If you can clarify, I think it will be easier!

Your post doesn't make a lot of sense if you don't explain the actual requirements. A "k only" file can mean anything from exporting a separation as a bitmap or greyscale image or prepping a vector file specifically. And of course "high resolution" is just as vague. You need to be much more specific and provide exact specs.

Mylenium