  Let f be a computable function from finite sequences of 0's and 1's to real
numbers. We prove that strong f-randomness implies strong f-randomness relative
to a PA-degree. We also prove: if X is strongly f-random and Turing reducible
to Y where Y is Martin-L"of random relative to Z, then X is strongly f-random
relative to Z. In addition, we prove analogous propagation results for other
notions of partial randomness, including non-K-triviality and autocomplexity.
We prove that f-randomness relative to a PA-degree implies strong f-randomness,
hence f-randomness does not imply f-randomness relative to a PA-degree.
