Q:  Have we found exoplanets in all regions of the sky equally,
           or have we found many exoplanets in a few small regions?


         Clearly, there is one region where MOST of the exoplanets
         have been found, and several regions along a curving path
         in the sky which also feature more exoplanets than the 
         average.

         Why?

         The reason is "Kepler".  The Kepler spacecraft was designed
         specifically to find planets around other stars by the 
         transit method, as described in 

           http://spiff.rit.edu/classes/summer_solar/lectures/radvel_trans/radvel_trans.html#transit

         For the first three years of its mission, it stared at one
         little region of the sky, at coordinates (RA = 295, Dec = +49).
         In that region, it found thousands of planets, making the biggest
         blue splotch on the map.

         After those three years, the spacecraft switched to another
         mode of operation.  It would stare at a new region of the sky
         for one month, discover some planets, and move a short distance
         to another region, stare for a month, move again, and so on.
         The clumps of discoveries which lie along a curvy path in the
         map represent these "one month" regions of Kepler's study.