Boundaries between Approach/Departure and Center

There don't appear to be hard and fast boundaries. You can see Center
boundaries and freqs on an IFR enroute chart, but they overlap with
approach/departure boundaries. Who does what depends on the nature of
the flight. Low level instrument flights often get handed from one
approach to the next if they are close enough to each other.

Flying at bugsmasher levels from Chicago to Des Moines, IA I usually
talk to Chicago Departure, Chicago Center, then Rockford Approach, then
Moline Approach, then Cedar Rapids Approach, then Chicago Center, and
finally DSM approach.

Approach freqs are always provided on the Airport/Facilities Directory
and on Approach Charts. Many GPS units also carry both ATC and
approach/departure freqs in the database.