I have an academic question/challenge (with practical use): how small can a kernel bzImage get and still be a kernel? I'm soliciting results, suggestions, and ideas (but not useless feedback, thanks), to get the kernel size down to 50kb.

I've tried turning off support for everything that menuconfig allows (silly, I know, but I'm seriously looking for the lowest common denominator), and compiling with "standard" tools and libraries that Ubuntu provides results in a 500k image. Additionally enabling "Optimize for size" lowered this about 10%. I'm climbing the learning curve to discover how to compile against the uClibc libraries, which I suspect will have a big impact. But I'm interested in what is still there, being compiled, even when support for everything is disabled, and if (and how) I can get rid of that, too!!

I remember back when Linux kernels where just a couple of hundred kilobytes, like 300kb, back in the days when slackware was the first distro. But there wasn't support for as many drivers as today. You would have to disable support for all the hardware that you will not need and enable only module support for the hardware that you will use, especially the hard disk, video, keyboard, mouse and (very important) network card. As long as it is under 1mb it should be adequate for most embedded systems.

Not much comment on the rest of your post, but your kernel does not link against the C library, so this would not make any difference…

You can see the size of the resident kernel from the kernel map. That is, of course, its size when uncompressed, and it doesn't consider modules.

The kernel can be made quite small, but size is typically not something that one optimizes for.