The branching topology of ethylene polar copolymers was for the first time successfully controlled by copolymerization of ethylene with polar olefins using a palladium-bisimine chain-walking catalyst, in which ethylene pressure and comonomer concentration were used to control the competition between isomerization (chain-walking) and monomer insertion processes. Although the overall branching density changes very slightly, the topology of the copolymers becomes more dendritic as the ethylene pressure and comonomer feed concentration are decreasing. This provides a straightforward one-pot synthesis to access a full range of functional copolymers having controllable branching topologies. To demonstrate the utility of this methodology, dendritic functional copolymers having hydroxyl, epoxide, and carbohydrate groups were prepared in a one-pot polymerization as potential functional materials.