Old posts in drop-down menus

When titling a post in forums (fora?), I often get a drop down menu showing similar titles from past posts.
On ZDNet the list is getting lengthy.

In general, are those saved on the host or on my pc?
If on my pc, is there any way to delete them? Be good if MRU Blaster did the job.
In fact, even if the old titles are on the forum host, I'd like to delete them.

Any information, assistance appreciated.