to hand it (i.e. the aforementioned item) to (sb)

to present; to give; to hand over; to hand in; to lay before

progressively increasing

to ascend progressively

to increase by degrees; in increasing order; incremental; progressive

to transmit; to pass on to sb else; (math.) transitive

express delivery

to present; to submit

delivery (of mail)

to make a special delivery; to courier