We study a slotted version of the Aloha Medium Access (MAC) protocol in a Mobile Ad-hoc Network (MANET). Our model features transmitters randomly located in the Euclidean plane, according to a Poisson point process and a set of receivers representing the next-hop from every transmitter. We concentrate on the so-called outage scenario, where a successful transmission requires a Signal-to-Interference-and-Noise (SINR) larger than some threshold. We analyze the local delays in such a network, namely the number of times slots required for nodes to transmit a packet to their prescribed next-hop receivers. The analysis depends very much on the receiver scenario and on the variability of the fading. In most cases, each node has finite-mean geometric random delay and thus a positive next hop throughput. However, the spatial (or large population) averaging of these individual finite mean-delays leads to infinite values in several practical cases, including the Rayleigh fading and positive thermal noise case. In some cases it exhibits an interesting phase transition phenomenon where the spatial average is finite when certain model parameters (receiver distance, thermal noise, Aloha medium access probability) are below a threshold and infinite above. To the best of our knowledge, this phenomenon, which we propose to call the wireless contention phase transition, has not been discussed in the literature. We comment on the relationships between the above facts and the heavy tails found in the so-called "RESTART" algorithm. We argue that the spatial average of the mean local delays is infinite primarily because of the outage logic, where one transmits full packets at time slots when the receiver is covered at the required SINR and where one wastes all the other time slots. This results in the "RESTART" mechanism, which in turn explains why we have infinite spatial average. Adaptive coding offers another nice way of breaking the outage/RESTART logic. We show examples where the average delays are finite in the adaptive coding case, whereas they are infinite in the outage case.