This paper is intended to provide insight into the controlling mechanisms of karst genesis based on an advanced modeling approach covering the characteristic hydraulics in karst systems, the dissolution kinetics, and the associated temporal decrease in flow resistance. Karst water hydraulics is strongly governed by the interaction between a highly conductive low storage conduit network and a low-conductive high-storage rock matrix under variable boundary conditions. Only if this coupling of flow mechanisms is considered can an appropriate representation of other relevant processes be achieved, e.g., carbonate dissolution, transport of dissolved solids, and limited groundwater recharge. Here a parameter study performed with the numerical model Carbonate Aquifer Void Evolution (CAVE) is presented, which allows the simulation of the genesis of karst aquifers during geologic time periods. CAVE integrates several important features relevant for different scenarios of karst evolution: (1) the complex hydraulic interplay between flow in the karst conduits and in the small fissures of the rock matrix, (2) laminar as well as turbulent flow conditions, (3) time-dependent and nonuniform recharge to both flow systems, (4) the widening of the conduits accounting for appropriate physicochemical relationships governing calcite dissolution kinetics. This is achieved by predefining an initial network of karst conduits (protoconduits) which are allowed to grow according to the amount of aggressive water available due to hydraulic boundary conditions. The increase in conduit transmissivity is associated with an increase in conduit diameters while the conductivity of the fissured system is assumed to be constant in time. The importance of various parameters controlling karst genesis is demonstrated in a parameter study covering the recharge distribution, the upgradient boundary conditions for the conduit system, and the hydraulic coupling between the conduit network and the rock matrix. In particular, it is shown that conduit diameters increase in downgradient or upgradient direction depending on the spatial distribution (local versus uniform) of the recharge component which directly enters the conduit system.