The following algorithm provides uniformly distributed partitions, assuming that it is possible to generate uniformly distributed random numbers over a continuous range (or, at least, over a discrete range with sufficiently many possible values that the odds of duplication are negligible).
To produce a partition of t into k values:
Generate k-1 uniformly distributed values in the range [0, t].
Sort them, and add 0 at the beginning and t at the end.
Use the adjacent differences as the partition.
