Q:

What happens if i block the centre of the rear element

For example here is a rear element with a filled in circle in the middle. 

What happens to the picture?  Is there image quality degradation?  Do I lose part of the picture?  What about amount off light transmitted? 
How do you calculate the effective aperture in terms of light transmitted when something like this happens. 

A:

It varies based on several factors:

Focal length: Same sized obstructions on the rear elements of telephoto lenses show up more than on the rear elements of wide angle lenses. 
Aperture: Same sized obstructions in the center of the rear element will show up more at smaller apertures than at larger ones. 

Roger Cicala, the founder and chief lens guru at lensrentals.com wrote a fascinating blog post that delves into just how much something has to obstruct the optical path before it is noticeable in a photo.  There are several examples of what a shot taken with large pieces of paper stuck to the back of the lens looks like.