Do trees have genes for stopping growth?
The answer I got from Jan Kolář of Charles University:


  Traits of trees like height and mass are a result of the genes and
  environment. The determinative factor for the studied plants and
  animals is a big amount of various genes. When we get to know all the
  functions of all the genes, we should be able to determine the most
  important ones but for now we know just that gibberelin and auxin are
  very important for the growth of the tree, so we'll be looking for those
  genes which control the level of those hormones.
  
  In case of trees, a big part of the height they can grow are utterly
  mechanical factors. The stem and the main branches have to be enough
  strong not to break with their own weight and the roots have to be
  enough firmly rooted in the soil. This limit is determined mainly by
  genes that control the grow of the cell walls, their mechanical
  resistance etc.