The development of the similarity version of the heatfunctions for the laminar natural convection near a vertical wall, isothermal or under constant heat flux, is presented for the first time in this work. From the beginning, the similarity formulation of the problem is based on a given form for the streamfunction, the streamlines not being usually presented. In this work, they are presented and analyzed. The paths followed by mass and heat are given by the streamlines and heatlines, which give us well bordered and non-crossed corridors where mass and heat are flowing. When the heatfunction is properly made dimensionless, its dimensionless values are closely related with the Nusselt number. In an attempt to present results that qualitatively apply over a wide range of Prandtl numbers, the used similarity variables are somewhat different from the ones usual in natural convection.