Linux Devices asks the question "When will smartphones replace PDAs, laptops?" The article is quite interesting, and they point out that usability obstacles still remain. Those will need to be overcome to a degree before we see an explosion of smartphones used for the typical sorts of pda and laptop activities.
Personally, unless we include a separate "mini terminal" to go with the smartphone, I don't see a typical smartphone form factor replacing a large number of laptops. Many pdas might be replaced, but not all. So the real question might be "When will smartphones dominate pdas and laptops in the marketplace?"
I think that in about 5-10 years when we look back at this question, we will realize that our context and language was insufficient. There will be new categories of device, and some larger devices or small foldable/rollable/multipart devices will come onto the market with phone capabilities. At some point will be a little hard to know what to call a smartphone as opposed to a handheld computer with phone capabilities.
We might even end up with a base computing unit in our pocket or purse or briefcase, accessed with a small and light clamshell with various options for keyboard and display. Sort of a local client server system all on your person, and ultimately connected to the internet also. That would even allow people to potentially leave the terminal pieces of different form factors all over the office and home for different people to use as desired. You get to keep your main computing platform personal (as opposed to trusting the web with all your applications and data). And yet you can still move portions of what you do to the web as appropriate, e.g. for backup or shared activities or when massive horsepower or data storage capabilities are needed.
But that is only one vision of a possible mobile future that I have created out of my imagination. There are many more possibilities that we have yet to imagine. And I'd bet that most scenarios are going to look a bit different than the sort of picture we currently have in our head when we think of smartphones. It might just be a moot point to talk about smartphone dominance if other form factors take over in the future.
As I always say about the future of mobile computing... "time will tell!"