We study support for unmanned aerial vehicle (UAV) communications through a cell-free massive MIMO architecture, wherein a large number of access points (APs) is deployed in place of large co-located massive MIMO arrays. We consider also a variation of the pure cell-free architecture by applying a user-centric association approach, where each user is served only from a subset of APs in the network. Under the general assumption that the propagation channel between the mobile stations, either UAVs or ground users (GUEs), and the APs follows a Ricean distribution, we derive closed-form spectral efficiency lower bounds for uplink and downlink with linear minimum mean square error channel estimation. We consider several power allocation and user scheduling strategies for such a system, and, among these, also minimum-rate maximizing power allocation strategies to improve the system fairness. Our numerical results reveal that cell-free massive MIMO architecture and its low-complexity user-centric alternative may provide better performance than a traditional multi-cell massive MIMO network deployment.