A numerical parametric study on positive diffuse discharges in pointto-plane geometry in air at atmospheric pressure is presented. Different discharge characteristics are studied: ignition time, connection time to the grounded cathode plane, shape of the discharge and its maximum radius at the connection time, evolution of the maximum electric field in the discharge front and velocity of the ionization front during its propagation. First, a case at a DC voltage of 50 kV applied on a rod anode ended by a semi-sphere with a radius of 100 µm set at 1.6 cm from a grounded cathode plane is considered. The influence of the rod radius, the position of a disc holder, the shape of the anode electrode and the radial extension of the computational domain are studied. The radius of curvature of the anode tip (varied between 100 and 1000 µm) and the shape of the anode electrode (rod or hyperbola) are shown to have a negligible influence on discharge characteristics. Conversely, the presence of a disc holder or a small radial computational domain lead to a decrease of the maximum discharge radius at the connection time and a change in the discharge shape from a conical to an ellipsoidal shape. These changes on the discharge morphology have only a limited impact on the propagation velocity of the discharge front and maximum electric field on the discharge axis. Then, a point-to-plane geometry with a rod electrode of 50 µm radius, in a 1.6 cm gap, with a 100 kV voltage applied with a rise time of 1 ns is studied. The influence of a disc holder on the discharge characteristics is the same as for lower DC voltages. Finally, the time evolution of the absolute value of the electric field at different test points on the discharge axis is studied. Close to the anode tip, rapidly after the peak of electric field due to the passage of the ionization front, the electric field in the discharge channel is shown to increase to values higher than the breakdown field.