WordNet sense 1 (administer or bestow, as in small portions):

administer, allot, deal, dispense, lot, deal out, dole out, mete out, parcel out, shell out, dish out

WordNet sense 2 (give out):

pass out, give out

WordNet sense 3 (cause to be distributed):

circulate, pass on, pass around

WordNet sense 4 (to arrange in a systematic order):

stagger

WordNet sense 5 (distribute or disperse widely):

spread

WordNet sense 6 (cause to become widely known):

broadcast, circularize, diffuse, disperse, disseminate, propagate, circularise, diffuse