If you park a toon at each of the neutral auctioneers -- I have a character set called 'Transfer', configured in IS Boxer for this.... you can observe that no one else is near a neutral auctioneer, and that transfers are safe.

The regular auction house charges a listing fee, based on the merchant price of the item. It also charges a fee of 5% of the sale price of the item. If the item is sold, the listing fee is refunded.

The neutral auction house is the same in this regard, except that listing and sale fees are 3x higher then the Alliance or Horde AH's.

If your item is listed for 1 copper, ideally a 12 hour auction so you can list more auctions before your toons run out of their deposit fund, it only costs 1 copper on the recipients end to purchase the item. The listing toon does not lose anything to the AH cut, and since the item was sold gets the listing fee back.

You just need to make sure you cover all of the neutral auctioneers, so no one can buy your epic gems (or Frostweave Bags, Enchanting mats etc) for 1 copper each.

There is a neutral AH in Everlook (Winterspring), Gadgetzan (Tanaris) and two in Booty Bay (Stranglethorn Vale). The BB ones are a) by the bank; and b) in the lowest level of the house closest to the upside down rowboat.