Equilibrium states of anodic double layers that form near a positively biased disk-shaped electrode immersed in a partially ionized plasma are studied experimentally using electrostatic probes. When the potential drop from the electrode to the plasma is less than a critical value, φ c , an anode glow is observed where a double layer potential drop is within a few millimeters of the electrode surface. For larger biases an anode spot forms where the double layer potential drop is centimeters from the electrode and the intervening region is a plasma more luminous than the bulk plasma. A theoretical model is developed which predicts that φ c ∝ 1/P + C, where P is the neutral pressure and C is a constant, and it predicts hysteresis in the current-voltage characteristic at the electrode; both effects are observed experimentally. The model also provides an estimate for the distance between the electrode and double layer potential drop that agrees with the measurements. Near small electrodes, anode spots are observed to be 'fireballs,' which are spherical in shape. Near larger electrodes 'firerods' are found instead, which have a cylindrical shape. It is shown that firerods are required by global current balance because they have a smaller effective electron collecting area than fireballs. Experiments also confirm that global nonambipolar flow (Baalrud S D et al 2007 Phys. Plasmas 14 042109) accompanies firerods. In this case all electrons are lost through the firerod to the electrode, while all positive ions are lost to the other plasma boundaries.