Traditionally, the capacity region of a coherent fading multiple access channel (MAC) is analyzed in two popular contexts. In the first, a centralized system with full channel state information at the transmitters (CSIT) is assumed, and the communication parameters like transmit power and data-rate are jointly chosen for every fading vector realization. On the other hand, in fast-fading links with distributed CSIT, the lack of full CSI is compensated by performing ergodic averaging over sufficiently many channel realizations. Notice that the distributed CSI may necessitate decentralized power-control for optimal data-transfer. Apart from these two models, the case of slow-fading links and distributed CSIT, though relevant to many systems, has received much less attention. In this paper, a block-fading AWGN MAC with full CSI at the receiver and distributed CSI at the transmitters is considered. The links undergo independent fading, but otherwise have arbitrary fading distributions. The channel statistics and respective long-term average transmit powers are known to all parties. We first consider the case where each encoder has knowledge only of its own link quality, and not of others. For this model, we compute the adaptive capacity region, i.e. the collection of average rate-tuples under block-wise coding/decoding such that the rate-tuple for every fading realization is inside the instantaneous MAC capacity region. The key step in our solution is an optimal rate allocation function for any given set of distributed power control laws at the transmitters. This also allows us to characterize the optimal power control for a wide class of fading models. Further extensions are also proposed to account for more general CSI availability at the transmitters.