For a function f with finitely many singularities, best uniform rational approximants of degree n on a compact subset K of the analyticity domain have n-th root error converging to exp(-2/C), where C is the capacity of the condenser (K, F) with F the set of minimum Green capacity in K outside of which f is single-valued. Moreover, counting measures of poles of best approximants converge to the Green equilibrium distribution on F.