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Abstract We examine vortices in Abelian Chern-Simons theory coupled to a relativistic scalar field with a chemical potential for particle number or U(1) charge. The Gauss constraint requires chemical potential for the local symmetry to be accompanied by a constant background charge density/magnetic field. Focussing attention on power law scalar potentials ∼ |Φ|2s which do not support vortex configurations in vacuum but do so at finite chemical potential, we numerically study classical vortex solutions for large winding number |n| ≫ 1. The solutions depending on a single dimensionless parameter α, behave as uniform incompressible droplets with radius ∼ α n $$ \sim \sqrt{\alpha \left|n\right|} $$ , and energy scaling linearly with |n|, independent of coupling constant. In all cases, the vortices transition from type I to type II at a critical value of the dimensionless parameter, α c = s s − 1 $$ {\alpha}_c=\frac{s}{s-1} $$ , which we confirm with analytical arguments and numerical methods.