Distribute, dispense, divide, deal, dole are comparable when they mean to give out, usually in shares, to each member of a group.
Distribute implies either an apportioning among many by separation of something into parts, units, or amounts, and by assigning each part, unit, or amount to the proper person or place, or a scattering or spreading more or less evenly over an area.
Dispense (see also ADMINISTER 1) differs from distribute in not usually implying a spreading out that affects a large number or a separation that reduces the size or amount of each part or portion; rather, it suggests the giving of a carefully weighed or measured portion to each of a group as a right or as due, or as accordant to need.
Divide (see also SEPARATE) stresses the separation of a whole into parts but it implies as the purpose of that separation a dispensing of those parts to, or a sharing of them by, each of a group; the term usually implies, if the context gives no further information, that the parts are equal.
Deal (usually followed by out) emphasizes the delivery of something piece by piece, or in suitable portions, especially to those who have a right to expect it ideal the cards for a game of bridge) ideal out equipment and supplies to each soldier).
Often, the term carries no suggestion of distribution, and means little more than to give or deliver.
Dole (also frequently followed by out) may imply a dispensing of alms to the needy (dole out daily one thousand loaves of bread), but since in this sense it usually suggests a carefully measured portion, it often suggests scantiness or niggardliness in the amount dispensed and does not necessarily suggest a charitable intent.