While my chickens spend a good deal of time -- sometimes literally waiting in line for the favored nesting box -- my ducks often drop eggs wherever and quickly. I find eggs along the driveway, beside their swimming pool, in the amsonia bed, inside someone else's coop.
Mine have access to a large bowl of oyster shell that they share with the chickens when everyone is out during the day. Egg-laying sometimes takes some practice to get perfect.