While browsing through this thread again I noticed that on many of the hairs shown the lower edge of the hairstyle faded away, spoiling the realism in my opinion. This set me wondering how much effect the tip width setting had.

Some tests with a few hairs on a sphere showed that the hair was evenly tapered from root to tip which is ok if you are using the hair room to grow a grass prop but hair does not taper, and even the tips are cut off square by the hairdressers scissors.

 In the past I had just accepted that the tip width would be less than the root width, probably because that is the default when you create a new hair, but a few test renders have convinced me that the root and tip should be the same.