A karst system is generally difficult to characterize especially regarding its conduits pattern and morphology. Even though speleology allows to map the geometry of cave systems, a large part of karst conduit networks remains unreachable underground. In this study, we use a reactive transport model that simulates dissolution processes in fracture networks to investigate the effect of discrete fracture network (DFN) properties (i.e., anisotropy, connectivity, fracture intersection types) on incipient karst conduit geometry under different boundary conditions (constant hydraulic head versus constant flow rate conditions, directional versus concentrated recharge conditions). We focused on single fracture (with/without cementation) and ladder like fracture networks which are common on limestone. Results show that fracture network properties, play a major role in the final geometry and topology of the incipient karst conduit patterns. Also, the presence of cement on a single fracture favors tortuous and curvilinear wormholes, while the anisotropy of the fracture network favors the formation of anisotropic incipient karst geometries. Finally, the type of hydraulic BC remains a major factor that governs dissolution processes and thus incipient karst conduit geometry.