When is an Eee PC not an Eee PC? When it's the rumoured 12in, ultra-thin Asus ZX-series of course! Although, according to DigiTimes' sources of this snippet of information, while the system will carry styling akin to the Eee PC S101, it isn't being included under the Eee banner.
The apparent reason for that similarity of design is that supposedly the S101 itself was originally intended to sit as the smallest model of the ZX-series, rather than the highest-end Eee PC. Asus President Jerry Shen, however, emphasises that any system over a 10.xin form factor is not a netbook, at least in his consideration. 11in and above sided system, then, will fall under the Asus brand. That seems fairly reasonable to me.
Aside form its similarity in look and feel to the S101, there's no other information right now about the 12in ZX-series system, other than a suggested NT$30,000 (~£575) launch price. At that price it's probably a good thing the ZX isn't supposed to be a netbook!