Each computer will use the same B.Net email to log in.
There will be only one password.
On the same computer or with multiple computers, you will pick the account from a drop-down, which you wish to run for that window/region.

The only thing so far that sucks about it...
Is the authenticator security has improved and each code is only good once for an account.
With every account on the B.Net email considered one account.
So 2.5 minutes to log in, instead of broadcast/repeat six digits once.

I have five accounts on one authenticator at the moment.
And am holding off the B.Net conversion as long as possible.
I actually ordered two more authenticators as a precaution against the battery dying on my nice device.
Two more authenticators and then go with five B.Net accounts might be an option; shipping on authenticators costs more then the authenticators - they're cheap.
But account transfers are fast within a B.Net account, and slower across B.Net accounts.