Currently Being ModeratedApr 7, 2013 2:53 PM (in response to kadet2)
I don't know about HP printers specifically (I have an Epson). But in the analogous Epson situation, the printing would be done through the ePrint app. That printing would only be available for some specific applications; e.g., photos. Many applications (e.g., Mail) would not have a way to print.
AirPrint printers, on the other hand, do offer considerably more print options. In your case, that would involve purchasing a new printer.
Currently Being ModeratedApr 10, 2013 12:52 PM (in response to iLadyOK)
the HP Officejet 4500 does not support AirPrint however the HP ePrint app supports the printer.
If the app fails to locate your printer within the All tab, that may happen ue to lack of Bonjour support or wrong configuration of your router.
To better understand if your router supports such protocols as used by Bonjour please clarify its brand and model.