We study abelian repetitions in partial words. We investigate the avoidance of abelian pth powers in infinite partial words, for p greater than two (the case of p equal to two was studied in some recent papers). In particular, we ask, for a given p, what is the smallest alphabet size so that there exists an infinite word with finitely or infinitely many holes that avoids abelian pth powers. We also investigate the problem of arbitrary insertion of holes into an infinite full word. We prove that if we insert arbitrarily many holes into an infinite abelian pfree full word, the resulting partial word is no longer abelian pfree.
Keywords: Combinatorics on Words; Partial Words; Abelian Repetitions.


