All covariant time operators with normalized probability distribution are
derived. Symmetry criteria are invoked to arrive at a unique expression for a
given Hamiltonian. As an application, a well known result for the arrival time
distribution of a free particle is generalized and extended. Interestingly, the
resulting arrival time distribution operator is connected to a particular,
positive, quantization of the classical current. For particles in a potential
we also introduce and study the notion of conditional arrival-time
distribution