Mammalian tissue comprises a plethora of hierarchically organized channel networks that serve as routes for the exchange of liquids, nutrients, bio-chemical cues or electrical signals, such as blood vessels, nerve fibers, or lymphatic conduits. Despite differences in function and size, the networks exhibit a similar, highly branched morphology with dendritic extensions. Mimicking such hierarchical networks represents a milestone in the biofabrication of tissues and organs. Work to date has focused primarily on the replication of the vasculature. Despite initial progress, reproducing such structures across scales and increasing biofabrication efficiency remain a challenge. In this work, we present a new biofabrication method that takes advantage of the viscous fingering phenomenon. Using flexographic printing, highly branched, inter-connective channel structures with stochastic, biomimetic distribution and dendritic extensions can be fabricated with unprecedented efficiency. Using gelatin (5%–35%) as resolvable sacrificial material, the feasability of the proposed method is demonstrated on the example of a vascular network. By selectively adjusting the printing velocity (0.2–1.5 m s−1), the anilox roller dip volume (4.5–24 ml m−2) as well as the shear viscosity of the printing material used (10–900 mPas), the width of the structures produced (30–400 µm) as well as their distance (200–600 µm) can be specifically determined. In addition to the flexible morphology, the high scalability (2500–25 000 mm2) and speed (1.5 m s−1) of the biofabrication process represents an important unique selling point. Printing parameters and hydrogel formulations are investigated and tuned towards a process window for controlled fabrication of channels that mimic the morphology of small blood vessels and capillaries. Subsequently, the resolvable structures were casted in a hydrogel matrix enabling bulk environments with integrated channels. The perfusability of the branched, inter-connective structures was successfully demonstrated. The fabricated networks hold great potential to enable nutrient supply in thick vascularized tissues or perfused organ-on-a-chip systems. In the future, the concept can be further optimized and expanded towards large-scale and cost-efficient biofabrication of vascular, lymphatic or neural networks for tissue engineering and regenerative medicine.