When doing n-tier development how do you guys handle the connection to the database?

Let's say my app is connecting to database on server A and the business logic tier is in server B.

Before in the client server world each workstation would run the EXE and establish 1 connection and use this connection thru the life of the application.

Now in the n-tier world the connection is being established at the business logic layer? Does that mean that's it's going to be opening and closing connections with each request?