A method of depositing an asphalt mat on a surface to be paved comprising the following steps: a) making a first pass over said surface to be paved so that a scanning means obtains and stores a topographical profile of said surface to be paved, b) accurately positioning a paving machine at a starting point of said topographical profile of said surface to be paved, c) loading asphalt into a hopper of said paving machine, d) causing asphalt to flow into an inner dispensing chamber of said paving machine, and e) utilizing said topographical profile of said surface to be paved to vary a flow rate of said asphalt out of said dispensing chamber, thereby depositing an asphalt mat of a thickness that varies along a width of said mat as well as longitudinally along said mat; and characterized in that i) a variable screed is positioned at a mouth of said dispensing chamber with individual plates of the variable screed being arranged to move between greater and lesser distances away from the surface of the subgrade in order to peel away a lesser or greater amount of excess asphalt from the mat, thereby to control said flow rate of said asphalt out of said dispensing chamber; and ii) multiple restrictor plates are positioned at the top rear edge of the dispensing chamber in front of an outlet of said dispensing chamber, the restrictor plates having the same width as the individual screed plates and being driven so that they slide fore and aft in conjunction with corresponding screed plates such that as an individual screed plate moves down to a lesser distance from the surface of the subgrade, the corresponding restrictor plate will be retracted allowing more asphalt material to be removed from the mat. a) making a first pass over said surface to be paved so that a scanning means obtains and stores a topographical profile of said surface to be paved, b) accurately positioning a paving machine at a starting point of said topographical profile of said surface to be paved, c) loading asphalt into a hopper of said paving machine, d) causing asphalt to flow into an inner dispensing chamber of said paving machine, and e) utilizing said topographical profile of said surface to be paved to vary a flow rate of said asphalt out of said dispensing chamber, thereby depositing an asphalt mat of a thickness that varies along a width of said mat as well as longitudinally along said mat; and i) a variable screed is positioned at a mouth of said dispensing chamber with individual plates of the variable screed being arranged to move between greater and lesser distances away from the surface of the subgrade in order to peel away a lesser or greater amount of excess asphalt from the mat, thereby to control said flow rate of said asphalt out of said dispensing chamber; and ii) multiple restrictor plates are positioned at the top rear edge of the dispensing chamber in front of an outlet of said dispensing chamber, the restrictor plates having the same width as the individual screed plates and being driven so that they slide fore and aft in conjunction with corresponding screed plates such that as an individual screed plate moves down to a lesser distance from the surface of the subgrade, the corresponding restrictor plate will be retracted allowing more asphalt material to be removed from the mat.