Google's official Chrome builds update themselves automatically while they're running without needing to relaunch.
The Mac Developer community has standardized on Sparkle, where the app downloads an update feed from the developer's site and prompts for an automatic update/install/relaunch.
To get the Chromium on Ubuntu behavior of manually-initiated centralized automatic updates, you'd have to use a package manager and the only viable one is MacPorts, which is just not a good fit for desktop software.
The Mac Developer community has standardized on Sparkle, where the app downloads an update feed from the developer's site and prompts for an automatic update/install/relaunch.
To get the Chromium on Ubuntu behavior of manually-initiated centralized automatic updates, you'd have to use a package manager and the only viable one is MacPorts, which is just not a good fit for desktop software.