  The Takayasu aggregation model is a paradigmatic model of aggregation with
mass injection, known to exhibit a power law distribution of mass over a range
which grows in time. Working in one dimension we find that the mass profile in
addition shows distinctive {\it dynamic condensates} which collectively hold a
substantial portion of the mass (approximately $80\%$ when injection and
diffusion rates are equal) and lead to a substantial hump in the scaled
distribution. To track these, we monitor the largest mass within a growing
coarsening length. An interesting outcome of extremal statistics is that the
mean of the globally largest mass in a finite system grows as a power law in
time, modulated by strong multiplicative logarithms in both time and system
size. At very long times in a finite system, the state consists of a
power-law-distributed background with a condensate whose mass increases
linearly with time.
