The present invention relates to a microstructure arrangement for the bubble-free filling with a liquid of at least one system for draining off liquids. The arrangement has an inlet for the arrangement to be connected to a system for the supply of liquids and at least one outlet for the arrangement to be connected to the at least one liquid-discharging system. The arrangement has a transition region, through which the liquid can be transported from the inlet to the at least one outlet. At a start of the transition region, at least one first microstructure element for producing a point with increased capillary force is provided, in order to achieve gap-free wetting of the areas bounding this point with increased capillary force, in particular side walls, a cover and/or a bottom.