Don't use phpmyadmin for anything. Ever.
It's simply not capable of dealing with realistic-sized databases correctly.
The command line tools are going to work. Phpmyadmin will probably not.
There is no size limit. If you want to split it up, the easiest way is to split it by table - simply restore it into another server (say, your development machine), then run mysqldump several times to dump out individual tables or sets of tables.
Mark