I'm asking this as a general discussion question, not a "how do I run Debian on my xyz phone/tablet/whatever".
Many years ago I used a mix of PDP11s and super-duper shiny new Sun workstations (then running, pretty much, BSD) at work, and an early PC with DOS on it at home. I really didn't like DOS much and for a while used an old PDP that work chucked out, though overall that wasn't great either. And then along came Linux, and like lots of other people, I thought it was great stuff. I remember early days using X when you had to play with all sorts of tedious configurations, including needing to know stuff like the sync and refresh rates of the monitor, but it was worth it to get a decent OS running on a personal machine. I switched from Slakware to Debian fairly early on and have used the latter for many years now. I still like it for the same reason I liked it back at the beginning: it lets me do things the way I want to do them. Grumbles about not liking new versions of Gnome have never bothered me because I don't have to use it: I install the basic minimum, add X and WM of choice (FVWM) and go from there.
I think, and I might be wrong, that the whole Linux thing snowballed to something enormously bigger than the likes of RMS or LT could ever have expected because of the way the PC did the same thing, equally to IBM's surprise. Suddenly everyone could own a computer, in fact lots of computers, they were so cheap, and although the bulk of them always ran a Microsoft OS, the Linux community was still a pretty substantial one. After a while, laptops came along, and at first it was a bit of a struggle to get Linux to run on them, but it could be done, and Linux adapted, and now you can install the system on most laptops with a few clicks.
And now, maybe, the next big change is happening, and the tablet computer has arrived. And just like laptops opened up an opportunity for mobile computing that did not exist before, tablets have opened up the possibility of having a usable computer (and I personally don't count a mobile phone in that category, they are simply too small for me to be able to use the screen) that you can carry around always and everywhere. And just as when laptops came along, and I wanted to run my OS of choice on them, I'd like to do that now, and that of course is a problem: the vast majority of tablets are based on ARM devices and, for the most part, Linux distros will only run on them in very basic versions, or not at all.
Sorry if all that seemed a bit long winded but I wanted to give some context to this. A bit of googling around reveals that I am not the only person who wants to do this: there are lots of questions about running Linux on tablets. I understand that there are things like hardware/firmware problems, but then there always were, and they got solved. Linux doesn't necessarily have to run on every tablet out there, just like it doesn't run on every PC: there will always be some very new or very cheap models with hardware that is not supported, but there are also many tablets using, I would imagine, pretty standard components.
I now seem to have gone full circle. I use Debian at work and at home, and on the train on my laptop, but out and about with my tablet, I don't. Ok, I can use Android, and I have a Samsung tablet with Cyanogenmod on it so a bit of customisation is possible, but I don't like Android very much. It reminds me of Windows in a way: there are lots of things about it that you simply have to take or leave, the only difference being that Mr Google rather than Mr Gates decided how it was going to be. In fact, I have 2 tablets at the moment, one with Cyanogenmod on, and one with Windows 8 on it. On the Windows one, things like Firefox, which I use a lot, are actually a better experience than they are on Android, because it's the normal desktop version.
If the PC revolutionised computing, maybe the next revolution is the tablet (and smartphone). Should Debian specifically or Linux generally be on board? Will it be? At the moment, many distros seem to regard the ARM platform as a peripheral irritation.