This paper is concerned with a class of singular prey-taxis models in a
smooth bounded domain under homogeneous Neumann boundary conditions. The
main challenge of analysis is the possible singularity as the prey
density vanishes. Employing the technique of a priori assumption, the
comparison principle of differential equations and semigroup estimates,
we show that the singularity can be precluded if the intrinsic growth
rate of prey is suitably large and hence obtain the existence of global
classical bounded solutions. Moreover, the global stability of
co-existence and prey-only steady states with convergence rates is
established by the method of Lyapunov functionals.