Magnetic frustration and disorder are key ingredients to prevent the onset of magnetic order. In the disordered hexagonal double perovskite BaTi1/2Mn1/2O3, Mn4+ cations, with S = 3/2 spins, can either form highly correlated states of magnetic trimers or dimers or remain as weakly interacting orphan spins. At low temperature (T), the dimer response is negligible, and magnetism is dominated by the trimers and orphans. To explore the role of magnetic frustration, disorder and possibly of quantum fluctuations, the low-T magnetic properties of the remaining magnetic degrees of freedom of BaTi1/2Mn1/2O3 are investigated. Heat-capacity data and magnetic susceptibility display no evidence for a phase transition to a magnetically ordered phase but indicate the formation of a correlated spin state. The low-temperature spin dynamics of this state is then explored by mu SR experiments. The zero-field mu(+) relaxation rate data show no static magnetism down to T = 19 mK and longitudinal field experiments support as well that dynamic magnetism persists at low T. Our results are interpreted in terms of a spin-glass state which stems from a disordered lattice of orphans spins and trimers. A spin liquid state in BaTi1/2Mn1/2O3, however, is not excluded and is also discussed.