You cannot use phpmyadmin for large database tables.
If you have ssh account access, you can use
mysql -u[dbusername] -p[dbpassword] [dbname] < [filename.sql]
to make it run in batch mode.
An example will be:
mysql -u username -h localhost -ppassword < filename
You didn't say what platform you're on, but here are some examples if you're on Windows:
Open a DOS prompt:
c:\mysql\bin > mysql -u Username -pPassword -e "source c:\windows\desktop\filename.txt" dbName
The command should be self-explanatory, except maybe for the -e modifier. The -e means, --execute=... Execute command and quit.
What if you have a database with data, and you want to populate another database (located on a remote machine) with the same data?
c:\mysql\bin > mysqldump --opt -u username -pPassword database | mysql -u username -pPassword --host=remote-host-ip -C database
You must have a login account on the remote server of course. Let's say the ip address of the remote machine is 127.204.19.121, the database is called UserAccounts, username/password is malthus/theory. Your query then would be:
c:\mysql\bin > mysqldump --opt -u malthus -ptheory UserAccounts | mysql -u malthus -ptheory --host=127.204.19.121 -C UserAccounts