In the last decade, there has been a tremendous increase in both the number of mobile devices and the consumer demand for mobile data communication. As a general network architecture, ad hoc mobile networks are expected to offload a large amount of mobile traffic in lots of promising application scenarios. However, how to achieve a good balance between delivery performances (like delivery delay and delivery probability) and network resource consumptions (like power energy and buffer storage) remains an extremely challenging problem. In this paper, we focus on the general k-hop relay routing, which covers a lot of popular routing schemes as special cases, such as the direct transmission (k = 1), the two-hop relay algorithm (k = 2), and the epidemic routing (k = n - 1). We first develop absorbing continuous-time Markov chain models to characterize the complicated message delivery process under the general k-hop relay routing, and then conduct Markovian analysis to derive all the above important performance metrics. Finally, extensive numerical results are presented to illustrate the achievable delivery performances under the general k-hop relay and the possible performance trade-offs there.