I have a Thinkpad X220 Tablet, if I am not wrong is that they call a "convertible" laptop.
There will be the possibility to use Ubuntu on Tablet (or even Ubuntu for Phones) with this kind of laptops in order to get full advantage from both the laptop and tablet features?
Up to now, due to the lack of user experience (scrolling ,zooming, hand gestures, pointer, bugs in the workspace window positioning while rotating) I use the tablet feature only to sign pdf with the embedded pen.
I am aware of this topic: "Will Ubuntu Touch work on my tablet or phone?" but it misses the "convertible laptop" category.
I also have been looking for a way to do this. It seems to me (although I am no expert) that it should be fairly straightforward to compile the "Ubuntu for Tablets" code for other processor architectures such as the intel one in your x220. Someone else will have to answer whether that actually is possible and how it might be done.
update: So basically I think your question is covered in this question Will there be x86 builds of Ubuntu Tablet / Phone?
The Thinkpad X220 Tablet only has the Touchscreen feature, the way it turns the screen to better suit a Tablet device and the word "tablet" in the name. The rest of it is a common laptop.
It has a normal Intel Core i5 processor. Uses the Intel HD Video and everything else a laptop would have.
It is a tablet in the way that it folds into one and the touchscreen support on it. But that is just about it. Since Ubuntu for Phone/Tablet is ARM oriented (And the Thinkpad X220 is not ARM but a normal Laptop Processor) it will not work correctly on the laptop. It would be best to suggest installing the Ubuntu Desktop on it than the ARM one.
For example, the link you provided to the other question shows all devices that use an ARM architecture, whereas this one does not. I know the confusion because of the twisting monitor, the word "Tablet" and the touchscreen.