  We prove the dimension of any asymptotic cone over a metric space X does not
exceed the asymptotic Assouad-Nagata dimension of X. This improves a result of
Dranishnikov and Smith who showed that dim(Y) does not exceed asymptotic
Assouad-Nagata dimension of X for all separable subsets Y of special asymptotic
cones of X over an exponential ultrafilter.
  We also show that Assouad-Nagata dimension of the discrete Heisenberg group
equals its asymptotic dimension.
