The asymptotic performances of multibranch diversity reception systems employing the popular and important combining techniques over arbitrarily correlated Rician channels are studied. Based on an integral representation of the joint probability density function of multivariate Rician random variables with arbitrary correlations, closed-form expressions for asymptotic error rate and asymptotic outage probability are derived for multibranch receiver diversity receptions. The important diversity schemes studied are maximal ratio combining, equal gain combining, selection combining, and hybrid maximal ratio combining as well as hybrid equal gain combining. Numerical results indicate that these analytical solutions can provide accurate estimation of error rate and outage probability in large-signal-to-noise-ratio regimes. The analysis provides some important theoretical and practical results concerning the performance characteristics of multibranch diversity receivers operating on arbitrarily correlated Rician fading channels.