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Anytime USENET has a problem with propagation, you might
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Remaining "logged in", would be implemented with cookies.
A cookie is stored locally, on your device. So if the iPhone
had a web browser, you wished to remain "logged in", the cookie
stored on the iPhone disk would have a copy of that cookie.
Now, if you step over to your home PC, it does not have that cookie.
If you enter username/password and request staying "logged in",
now your home PC has a cookie.
Now, say you step across to the iPhone again. You go to Google
with the browser. Now, Google keeps track of your logins, and
knows the last login was from the home PC. There is no reason
for the iPhone cookie to be considered valid at that point in
time. (it is up to Google, to develop a policy of whether
they accept the cookie at that point or not.)
So you can see from the approach used, that the cookie is
hardly ever going to save you much time. Unless, you *stay*
on one device, and do your browsing with the *same* browser
all the time. Then, just maybe, that cookie will work.