Zone Mail, commonly referred to as zMail, is the in-game mailing system on AMZ.
On the old AMZ, you could have 30 pieces of mail in your inventory and another 30 saved. You could also access your friends list via zMail.
There is no limit as to how many zMails you can have in your inbox. You also have an outbox, a sent folder, so you can keep track of your sent messages. The sent folder was added on the 8th of November. Just like the Old AMZ, you can access your Buddies list through zMail.
Strangely enough, on the New AMZ, nowhere is the mailing system actually referred to as zMail.