I think it makes sense to zoom to the middle.

Since you're using this with one hand, tapping anywhere other than the area where your thumb naturally rests would be uncomfortable.

Also, and more importantly I think, what if you wanted to zoom in to a position near the top of the screen? You would have to tap near the top of the screen and move your finger up, causing your thumb to go off the screen. So you wouldn't be able to zoom in to an area near the top of the screen or zoom out from an area near the bottom. If such a large segment of the screen is unusable for this feature, you might as well just have it zoom to the middle, and make the user center the place they want to zoom to on their own.