Since unregistered emails seem to be rising in popularity again, I thought I might post two of my older guides here.
i. Method to Obtain Target Emails.
Guessing random emails is going to get you no where. Sure, maybe one in a hundred+ might actually work, but if those odds are good for you, go ahead.
Google.
Google is powerful tool. I don't want to go into much on this, as I use this method for my own purposes. If you know what your doing, you should have no problem at all finding mass emails related to neopets.
Hash Lists.
The most popular, non-released method I think. Don't ask me what this is or where to get one (Again Google, I found many free ones by simply googling), as discussion of it is not permitted. The only thing that's useful about this list, is it contains a lot of emails, and for the most part they all should be connected to neopets accounts.
Once you have the list, pop the list into here :
(you need an account to see links)
Where it says "Separator", select New Line and hit Extract.
In the Output Window, you should now have a list of Emails.
The only big providers that actually purge their emails are ; Hotmail/Live, Yahoo, Gmail.
So you might want to use the filter option.
ii. Method to Obtain the Deleted Emails.
Once you have a lengthy list, about 100-200 should be fine, your ready to mass check for which ones can be recreated.
Go to your hotmail.
Create a new message, in the recipients, paste the list of emails you got from above (Limit is 100, or something around there).
Once you hit Send, you will get some emails stating "Delivery Status Notification (Failure)".
In the message, there will be some emails listed. These emails, not all, have been deleted.
iii. Fun Part.
Now that you have some uncreated emails, check with neopets to see which ones have neopets account attached. My odds with this are usually one in three. If they do indeed have a neopets account attached, recreate them, retrieve username/password, and

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Most Efficient Way to Grab Unregistered Emails from Google
Google is an all-powerful tool. You can harness its power to find thousands of unregistered hotmails pertaining to any niche you want.Overview :
You use various google dorks to search for Hotmails/Gmails/Yahoos on Google.
Once you find a nice dork, CRTL+A, paste the list
(you need an account to see links), and extract all the emails.
Continue doing that for however many pages you want (Option to optimize the search results to 100 per page).
Some emails may be a little messy like with a period at the end, just remove them manually or use like notepad tools.
And lastly you verify if there connected and available or not.