I partitioned a 1 GB boot partition when I installed 12.04. Every update that installs a new kernel adds to the content of the boot partition. Soon it will be filled. Does Ubuntu overwrite or purge old unused files in the boot partition automatically?
No, Ubuntu doesn't overwrite or purge old kernel versions or unused files automatically.
To remove old kernel versions and other unused files, you can use Ubuntu-Tweak. To install it run next commands in terminal (it is not available from the standard repositories):