If you're too impatient to wait for Samsung to get Android 4.4 to your carrier variant of the Galaxy Note 3 (or if you're just tired of TouchWiz), the indefatigable boys and girls of CyanogenMod are here to help. They've just released the first nightly builds of CM 11 (KitKat) for Samsung's plus-sized flagship, with support for the international LTE model (N9005), plus Verizon, T-Mobile, and Sprint versions.
As it happens, Samsung just started sending out the official 4.4 update for the N9005 earlier this week, so those of you who are on the unlocked version of the phone might want to go for the TouchWiz build of KitKat instead. American carriers will probably be at least a month behind, and possibly much longer, so those users will find the ROM more tempting. Of course switching to CyanogenMod means giving up Samsung's stylus-oriented apps and UI touches in favor of a more AOSP-style experience.
Regular ROM flashers, you know the drill: download the nightly build, load it up in your custom recovery, backup, flash, badda bing badda boom. Add some Gapps if you want the Google Play Store and associated goodies. As always, keep in mind that nightly builds are a little on the wonky side, though CyanogenMod's official nightlies tend to be more stable than most.
There is a distinct lack of both the international GSM and AT&T models in this initial rollout. I'm betting that the former is because all of the LTE variants share common hardware and code, while the latter is probably thanks to the locked bootloader on AT&T phones. We'll be sure to let you know if any more builds show up.