Linux distros that are designed to only/mainly get their rootfs over the network

• Linux Terminal Server Project
• lessdisks, promoted by a member of Portland FreeGeek
• Tiny Core (is able to boot PXE, apps are always downloaded from the network on an as-needed basis)

Linux distros that officially support mounting their rootfs over the network

• Ubuntu Live [nfsroot]
• SLAX [httpfs]
  syslinux.cfg has a "Slax as PXE server" boot option. This adds "autoexec=/boot/pxelinux.cfg/start;/boot/pxelinux.cfg/web/start;xconf;telinit~4" to the boot line. /boot/pxelinux.cfg/start starts DHCP and TFTP, and /boot/pxelinux.cfg/web/start starts the Monkey webserver.

Linux distros that don't support mounting rootfs over the network