The Dynamic Ergodic Divertor on TEXTOR imposes three-dimensional stochastic magnetic field lines in the plasma boundary. The resulting heat deposition patterns on the divertor surface depend strongly on a magnetic topology, including radial penetration of magnetic field lines within the first few toroidal revolutions. The influence of the collisionality in the plasma edge is of importance for the resulting deposition patterns. The heat flux formed by the electrons streaming along the field lines with shallow penetration is only seen at low collisionalities, while these field lines reach areas of low electron temperature. The other class of field lines penetrates relatively deep within the first few toroidal turns reaching the plasma region with much higher electron temperature, which makes parallel transport much more effective, even at the higher level of collisionality.