[citation][nom]back_by_demand[/nom]Your phone is a personal computer, you mean ATX don't you... just say "yes"[/citation]
A PC (personal computer) is a device in which you have the right to do whatever the hell you want with it, which also does computing.
A work computer is NOT a PC, as it is locked down to the demands of it's use. But it can be an ATX device
A work server is not a PC, but a home server can most definately be a PC, no matter the form factor
An ATM, POS, microwave, digital watch, or other single-purpose (or at least narrow purpose) computing devices are simply not PCs because you have little to no control over the behavior or function of the device
A cell phone purchased from a cell service provider which is locked into a contract is NOT a PC. You may have a great amount of control over the device, and it may have a wide focus of things that it can do, but ultimately your ability to make changes, and your ability to use the device is at the whim of the service provider, and you do not control or effectively own the device.
A Mac is not a PC, though the line is getting admittedly extremely blurry here. It is illegal to put an OS on a Mac other than OSX as the main OS. According to their EULA (not sure if this is current) you do not even have the rights to the hardware in order to make any changes (though they tend to let little things like Ram and HDDs slide).
Most unlocked phones, while extremely close to being PCs, are not PCs because you can only put a single OS on them.
The new WinRT tablets will not be PCs, as they are tied to windows, and you do not have the right as an enduser to make a change to a different OS if you would choose to. Some of the new Win8 hardware may also suffer the same fate.
However; All of these phones, tablets, Macs, and other devices are definitely Personal Devices (PD) in that they are for your personal use, and I am more than willing to have a few of these personal devices in my posession. But to think they are mine, to do with as I please and see fit, would be entirely wrong. These are closed systems that I am allowed to use within the constraints of the original designer, where as my PC is a fluid system of hardware components and software, which often changes, merges, and splits into and with other devices, other uses, and entirely other purposes. My first PC was built in 2001, and it evolved over the years through hardware failures, upgrades, changes in software packages, and various use models up until today. In fact, I used that same case from 2001 up until a year and a half ago. The case lived through win98, 98SE, 2K, XP, XP64, 7 Milestone 1&2&CP, 7 64bit, Win8 RP CP RTM, and some 10ish versions of linux. Sometimes these OSs stood alone, and other times there were several (up to 5 I think) on at one time because I needed various features of them for what I was trying to do. For hardware that single case went through 6 mobos, 3 power supplies, a host of GPUs, 3 sound cards, at least 10 HDDs, various fans coolers and light kits, and lots of other hardware. To complicate things further, I did not always use that case. For a while I moved into a slim ATX case, then back to the origonal when I moved out of the cramped apartment, then to a new case, and just recently to another case. Parts that had been in that origonal computer have moved on into computers of other family members, friends, neigbors, and even split into other computers for my own use. I also have 2 netbooks which have often shared or swapped parts on multiple occasions, and each survived through a few OS changes (7 32bit, 7 64bit, 2-3 linux distros, and win8 32 and 54bit). It is far more limited in what can be changed in them, but what is changeable is still mine to change, so they are most definitely PCs. I am also in the market for a smartphone, and I have this great debate of getting a PC style phone that can run android and windows mobile or windows phone, or getting a dedicated closed phone that simply works and that I don't have to think about much, getting a phone tied to a specific service is not an option, both would be personal devices, but only one is a PC.
A PC is a concept of use model, it is not a concept of a hardware platform.