Apparently the Ullambana Sutra does not have a sutta version as I had thought. I thought I had read a sutta version some time ago.
Try this one?http://www.accesstoinsight.org/tipitaka ... .than.html
EDIT: no specifics on prayers per say, but it does seem to explain the mechanism...
Food donations affect those in hungry ghost realms, where there are no other ways to eat.
I imagine Dharma/merit donations affect those in realms where there is no way to generate merit?
My understanding of merit dedication is that it and the action that generated the merit are both not only good causes, but good effects, a contributory cause being the condition of the deceased. In this way, a valid chain of cause and effect is maintained and thus the deceased would experience some effect. Not sure if that makes sense.