A flexible polymer film was coated with titanium oxide and a fluoroacrylate polymer to make the surface superhydrophobic and then patterned with superhydrophilic open microfluidic channels consisting of fractal branching structures. The lateral transport of liquid driven by the imbalance of the Laplace pressure in the flow channels with a width gradient allowed the collection of tiny aqueous droplets from the entire surface of the film at the converging point at the center within a second. The proposed fractal patterns were well-defined (i.e., mathematically determined in a unique manner) space-filling trees with only a few geometrical parameters. With the optimized geometrical parameters, the fluid volume collected to the film center (2.0 mm radius, 7.3% of total pattern area) reached 74% ± 9%, where the areal density of liquid was 12 times higher than that of an unpatterned surface.