In Super Mario Bros 3, how to make power-up items appear in Hammer Bros battles?

Sometimes, a power-up item (mushroom/flower/leaf) will appear when you hit one of the solid blocks during a battle against the Hammer Bros that patrol world maps on Super Mario Bros 3. If I recall correctly, when playing on my NES sometimes I would also hit an invisble block somewhere on the screen during battles against their versions which do not have visible blocks (like the Boomerang Bros).

I've never figured out what conditions trigger the availabity of such "secret" items during battles. Is it random or is there a way to make sure to collect them?

As I understand it you can "control" what items appear inside the blocks by entering the fight with them when they are in certain spaces on the map. This website has some details on that near the bottom and even has a helpful interactive map, but I haven't test myself to see how accurate they are. Let me know if you decide to test.