Several factors will play a role in the decision.
From a usability standpoint, with regard to Fitts's Law, buttons should be reasonably large and at the edge of the screen to take advantage of the "infinite edge", the idea that a cursor cannot go beyond the bounds of the monitor. In a mobile setting, however, the cursor is your fingertip and moves through three dimensional space so this is less relevant. Properly responsive sites usually only have one dimension of scrolling however, so the underlying ideas of Fitts still holds. If you put a button at the bottom or the top of the screen, in a fixed overlay or in the scrollable portion, the bottom and the top are still the best place, and should at least accommodate a thumb.
From an aesthetic standpoint, you don't want giant buttons taking up the whole screen. With smaller screens its reasonable to have a button of focus stretch horizontally, but as screens increase in horizontal size, beyond a certain width just seems silly and disproportionate. But you still want access from the edge. Often, mobile interaction is carried out with one hand. If the button can't be reached in a one-handed grasp (it's too small and at the center of the screen), then you may frustrate the user.
So maybe proportionate padding is the answer? Padding increases with the size of the screen, but only to a point so the button is still thumb accessible, assuming this is an important button that the user will be seeking out.