Sonavi
I think the n-tier is the bottom layer of detail. It is what the developers themselevs would usually do right before they sit down for an hour and code a unit of code (of small discreet function.)
This is not the role of the BA. This is the role of the programmer.
The same goes for designing the 3 tier application diagram for a new system. This is definitely not a usual job for a BA.
If on the other hand you are analysing an existing system you can use any number of tools. Tony Markos will recommend a data flow diagram, which will do the job just fine.
At the end of the day it can be pretty loose at the first pass. Even just lists of activties that happen at each layer.
The task you are doing is identifying the logical and physicl boundaries of components, and then their relationships.