The Mishna reports in Menachot 10:4 that, after the required amount of premium flour had been extracted from the barley set aside for the Omer, the considerable amount tof leftover, mixed-quality flour would be "redeemed and edible by anyone." It seems to me that such flour, which had been processed in the Temple and had come very close to being part of a unique annual national offering, would be a treasured substance. So, I'm wondering who, in practice, got to have it.
According to the first opinion cited in the mishna, that the flour was property of the Temple (hekdesh)1, then redeemed so anyone could eat it, who redeemed it? Was there a Temple outlet store for such items? Was there a one-time auction?
According to R' Akiva, who disputes the first opinion and implies2 that only the flour extracted for the Omer was ever made hekdesh, am I correct in understanding that the rest would just be returned to whoever owned the field the barley had been harvested from? It seems a little surprising that that fortunate person gets to have used the Temple as his grain-processor, in effect.
1. As indicated by the fact that according to this opinion, the leftovers are exempt from Ma'aser, which must be because the original harvest process put all the barley straight into hekdesh. (See R' Bartenura.)
2. As indicated by the fact that according to R' Akiva, the leftovers require Ma'aser. (See R' Bartenura.)