The asymptotic performance of multi-user amplify-and-forward relay networks with massive MIMO is investigated. By using transmit power scaling laws at the user nodes, the asymptotic signal-to-interference-plus-noise ratio (SINR) expressions are derived when the antenna counts at the relay and destination are allowed to grow unbound, and thereby, the asymptotic sum rate expressions are obtained. Notably, these asymptotic SINRs and sum rates are independent of the fast fading component of the wireless channel, and consequently, yield a low-complexity medium access control layer and reduced latency in the air interface. Further, the detrimental impact of practical transmission impairments, including (i) imperfect channel state information (CSI), (ii) co-channel interference (CCI), and (iii) pilot contamination is studied by deriving the corresponding asymptotic SINRs and sum rates. For the perfect CSI case, the transmit power at each user node can be scaled down inversely proportional to the antenna count at the relay without degrading the system performance. However, for the imperfect CSI case, the transmit powers of the user nodes can only be scaled down inversely proportional to the square-root of the number of relay antennas. Interestingly, for the perfect CSI case, the presence of CCI neither affects these transmit power scaling laws nor degrades the asymptotic SINR. However, pilot contamination significantly limits the system performance.