HI,
I actually have my box on the Mac version Unticked (it leaves the item on the server.)
I had the iPhone set to Never (remove) so it also leaves the message on the server.
I had understood that this was what you wanted - to display the same messages on multiple devices.
Having said that you could move closer to what you describe doing so that one login will remove those when downloaded (presuming that you would read them soon afterwards)
With two macs this may work if they are turned on at different times and "fetch" new mail individually.
With an iPhone that is connected all the time and fetching mail maybe more difficult.
My method does mean I do have to manually delete older emails from the servers involved from time to time.
Generally I have my three computer on but only one is logged in to Mail.
It does mean I can access Mail from my Laptop when travelling if required.
7:49 PM Wednesday; January 2, 2013
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.2)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad
"Limit the Logs to the Bits above Binary Images." No, Seriously