Additional cost for playing Battle.Net?

There will be no fee for battle.net. When you purchase SC2 you will receive a CD Key, this key will allow you to create One account to use online to play SC2.

It comes with a CD-Key. It also requires you to have a battle.net account, you can make one for free at battle.net. once you log in to battle.net you attach your CD-Key to your account and use that as your login to the online portion of the game

Battle.net access with Starcraft 2 can either be time limited, or unlimited depending on what region you live in.
Generally most people have the unlimited version which grants access to the game and battlenet with no additional fee, ala WoW.
However there are some regions they are planning on deploying a subscription based plan where, like WoW you pay on a regular basis for access to the game.

As for subscription access, it only applies in South Korea, and only in limited settings. They have the option of buying unlimited access for the same price we do. They also get free play if they have an active WoW subscription, can buy $1.50 day passes, pay $1 an hour in cybercafes, and buy $8 30-day passes.

So, no, there is no additional charge for playing the game if you buy the retail box, no matter where in the world you are.

Unless you count paying for your internet an additional cost, No they don't charge you for it, unless your region is time limited.

USA Release of Starcraft 2 comes with a CD-key

No payment is required to play online.

In case you were unaware, There is a CD-key that is attached (permanently) to a battle.net account (either you make one then, or use a pre-existing one).
No cost to play online.
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