Z signifies that the unit is being sold as a whitebook/barebone and not as an Asus ensemble, which means that customers can configure it as they like from a reseller, but also that the curstomer's warranty is through the reseller and not through Asus. 84 may have identified the chassis or the performance. Asus' numbering scheme has changed from numbers based on performance to numbers based on the chassis over the last couple years. J is Asus' designation for notebooks with the Intel 945 PM chipset and dedicated graphics. The p may signify Nvidia as the graphics brand.
You might want to ask the Linux compatibility questions in our Linux forum if you don't get a response here. I've got a Z71V and everything except the card reader works fine in Linux, including the special buttons. For more on support of special functions and options, check out
http://lapsus.berlios.de/
