Allot - to give someone part of an amount of something that is available, or to decide that something will be used for a specific purpose.
"How many students finished the test in the alloted time?"
P.S.For me "alloted" sounds similar to "limited in something"
Allocate - to officially give something to someone, or to decide that something can be used for a specific purpose.
" No agreement was reached on how much money should be allocated."
P.S. As for me, "to allocate" is close to "to give"
Distribute - to spread something over an area.
"The two men were convicted of distributing anti-government leaflets. "
P.S. "to distribute" has something from "to spread ".