If you are using the aol imap profile, you cannot selectively erase messages on your iphone only. You would need to re-setup your aol mail by using the "other" setting and specifying aol's pop client settings, then in your iphone you should be able to select the messages to delete there, but won't get deleted unitil you do it at your desktop. The Pop profile downloads the messages to your device, so if you erase them on your desktop, but not on your device (assuming you downloaded the message to your device first), then the message will not be deleted on your device. The imap profile basically syncs your device(s) to the server, that's why when you delete it off your iphone, it gets deleted from the server. Pop profiles do not synchronize to the server, that's why you can erase the message on your device and it will still be on the server, provided you clicked on the setting on your device to "NOT delete" messages on server after they have been downloaded.