Sorry for the delay but I have been checking this out with Doug. Compare with his posting on 13 April.

Here are my findings.

----
NOTE: I have Vuescan installed and it affects some of the following. It adds the 'EPSON' at the start of the Printer name and puts a (Scan) button at the top of my Print & Fax System Preferences.

 On the MacBook, within System Preferences>Print & Fax>Print tab, there an item 'Location'. It says 'Brian's iMac'.
Thus:

---- MacBook
EPSON Epson Stylus Photo TX710W @ Brian's iMac
then
Two drop-down menu items, (Open Print Queue) & (Options & Supplies)
Location:Brian's iMac [that's to me in another room]
Kind: EPSON SP TX710W Series@Brian's iMac
Status: Idle
----
Printer sharing - that should be a clue.

Looking at MY iMac Print & Fax I see:

---- iMac
EPSON Epson Stylus Photo TX710W [I am "Brian's iMac"]
then
Two drop-down menu items, (Open Print Queue) & (Options & Supplies)
Location:Brian's iMac [that's me in my room]
Kind: EPSON SP TX710W Series
Status: Idle
[√] Share this printer on the network (Sharing Preferences)
Default Printer: EPSON Epson Stylus Photo TX710W Series
Default paper size: A4.
----

The only cable connection to the printer is from my iMac.
My iMac has Airport turned Off.
There is NO hardware connection between the Time Capsule and the printer. It does nothing for printing.
It has its direct connection to the Internet by Ethernet cable and this is used by my iMac > Time Capsule ethernet cable or by the MacBook > Airport > Time Capsule.

The in-built Airport software on my iMac presumably operates as a 'Receiver', as you noted, and it gets its signal wirelessly from the MacBook but not through the Time Capsule.

If my iMac is turned off, the MacBook will not print as it cannot locate the printer.
"Sharing Printer's" is the clue.
Access, or lack thereof, to this Internet has nothing to do with this problem.

------------------------
Regards from brianF
===============

On 13/04/2011, at 7:40 AM, Jon Johanning wrote:

> On 4/11/11 10:30 PM, Brian Ferguson wrote:
>> However, it appears that her iBook uses its Airport link to my iMac and then to the printer. I assume that if I turn off the iMac she cannot print.
>> 
> I wouldn't swear to this, since I am no networking expert, but I think that if the iBook, iMac, and printer are all on one network, it wouldn't matter if the iMac were off -- but the Airport has to be on, of course. Try an experiment and see.
> 
> Regards,
> 
> Jon Johanning