What are some common mobile keyboard layout ergonomics design examples (or research)?

There is a very similar question regarding the layout of smartphone keyboards, which is just one aspect of what I am interested in finding out more about.

Even though there is no consistent way that people interact with their smartphone, and that applications allow different types of input, there is at least some consensus that people can either use their mobile phones with just one hand or with both hands.

Given that there is definitely enough people that would see using their mobile phone with just one hand, what are the considerations given in terms of even just the software design (which is more flexible) to address the ergonomics (e.g. soft keyboard placement, input entry, handedness, etc.).

Are there some common examples, research or even people looking into this aspect of software design?