The standard placement is 20 - 24 inches from the floor up to the center of the TP holder. New toilet configuration these days my be several inches higher than the old standard toilet. If you have a newer toilet, adjust accordingly.
Next to the toilet generally, could you be more specific? toilet paper dispensers
Paper dispenses up from the bottom not down from the top
The standard position for a toilet paper holder - should be 8-12 inches in front of the toilet and 26 inches (centerline) above the floor.
The toilet paper holder needs to be within easy and convenient reach of someone sitting on the toilet. There should be room between the person and the holder. Also, if possible, avoid placing the holder under the towel rack, since the paper could become wet. The practical way to figure this out is to sit on the toilet.
Toilet Paper Holder
Either on the left or right, 26 inches off the floor and 8 to 12 inches forward from the front of the toilet bowl. Reference: http://www.ehow.com/info_8027723_proper-placement-toilet-paper-holder.html
like 2 inch. or or smaller but it really doesn't matter
Joseph Gayetty invented toilet paper in 1857
It would probably be best if you had the toilet paper holder was within arm's reach. Actually it should be within reach of your arm furthest from the tissue holder so you can pull with your closest arm and tear with the other.
Back in the day when my toilet paper holder broke, I used a piece wire to insert into the paper roll and attached it to the sides of the toilet paper holder. This was a free, quick and easy way to keep using the holder and not spend any money.
toilet paper holder
Joseph Gayetty