I have a few questions.
1. could you boot directly from an online operating system using only bios and your network card?
2. If you cant. could you boot from a bootable floppy, cd, dvd, flash drive. etc that took up little space just enough to load network drivers and contact a url to connect to the online operating system that would download and run live in ram.

operating system should be about the size of xpud,puppy,dsl, slackware stuff ya know

I have experimented with a few but they all seem to need an os to use a web browser to use a lan or wireless card to use it in a browser. like glide os or amoebaos

If you mean over a WAN like the internet, then no. Over a LAN it is definitely possible, research PXE.

I have installed OS via network boot ,PXE,TFTP, you can give a Live CD to installation path and then do it.
SO on a LAN is definitely possible on internet if you can get path to Live CD for your TFTP then it might be possible I am not sure though never tried on internet.
Have done debootstrap etc but not without installation.

It would be possible to use a PXE server, and tell the PC to get it's info from an internet source. It would be so slow that it would be useless, and you would need a DHCP/PXE server running from the LAN anyway...

If you are able to use a USB drive anyway, why not install the entire thing only it? It might help if you tell us why you want to be able to do this.

Ya even I am curios to know why are you trying this?

YES plenty exist. As above pxe is the old way.
You can make your own setup too. The most simple is boot to a knoppix 5.x cd and start knoppix terminal server. The lan's can boot to ram if they have pxe or rom support in nic.


Start at netboot.me and see boot kernel org and I know there are a few others.

See gpxe (part of the old rom site).