  Consider a rowwise independent triangular array of gamma random variables
with varying parameters. Under several different conditions on the shape
parameter, we show that the sequence of row-maximums converges weakly after
linear or power transformation. Depending on the parameter combinations, we
obtain both Gumbel and non-Gumbel limits.
  The weak limits for maximum of the coordinates of certain Dirichlet vectors
of increasing dimension are also obtained using the gamma representation.
