My current prediction
From a comment I wrote when considering the current approaches from manufacturers.
I think in the short term apple will continue to dominate for one or 2 more years without a massive os change but after that android will overtake iOS if they don’t change. Then once intel gets its mobile processors up to scratch for real computing in a tablet (10 hours+ battery life with decent usage at nexus 7 size and i5 speeds, mid range graphics) if the current trajectory stays the same, ceteris paribus then I think Microsoft has a good chance of dominating but that’s so far in the future another company could have formed and revolutionised computing by then in 5 or more years or apple or google may have an os ready for desktop power computing. As power increases people will want more from their devices which in their current forms iOS and android are not ready to provide. While software will probably will have far better interfaces than they do now I believe that the current desktop only software will become portable friendly and then be adapted for a docking interface.
I can only see two reasons why this may not occur, the first being that no consumers want a device for serious portable work. For example why would I pay $1000 for a tablet when I can get by with a $200 one, with the majority of people only working at home or work making the extra investment not worthwhile and maybe the software not as simple eg for a technophobe to use. The other is if companies don't want their products to become so good that improvements and innovation become marginal in benefit not making a difference to most consumers. I think we can already see the economic effects in this with companies pushing for a subscription model. I think eventually you won't be able to buy anything outright, you'll either be advertised to or pay a subscription fee indefinitely and the whole industry will adopt one of those models to stay alive.