A general class of solutions is found for the resistive hydromagnetic equation. The results are applied to the case of a prescribed stagnation point flow. It is shown that general solutions with magnetic null points exist. Scaling laws for the length and the width of the current sheet of the solutions are given for the general case. It is shown that the length of the current sheet increases with magnetic Reynolds number unless the outflow boundary conditions prevent the sheet length from growing. The latter would result in the appearance of boundary layers in the outflow region.