distribute (something) over (something)
To apply something to something else somewhat evenly over an entire area. You need to distribute stain remover over the entire discolored area to have any hope of cleaning it.
distribute (something) to (someone)
To pass something out, usually to each person in a group. I'll have the volunteers distribute pamphlets to the audience before I begin my lecture.
distribute something over something
to spread something over something or over an area. Distribute the icing over the entire cake. Walter distributed the sand over the icy spots.
distribute something to someone
to give out something to someone. Can you distribute this clothing to the needy people who live around here? I will distribute the ice cream to the party guests.