Efficient exploration strategies are vital in tasks such as search-and-rescue missions and disaster surveying. Unmanned Aerial Vehicles (UAVs) have become particularly popular in such applications, promising to cover large areas at high speeds. Moreover, with the increasing maturity of onboard UAV perception, research focus has been shifting toward higher-level reasoning for single- and multi-robot missions. However, autonomous navigation and exploration of previously unknown large spaces still constitutes an open challenge, especially when the environment is cluttered and exhibits large and frequent occlusions due to high obstacle density, as is the case of forests. Moreover, the problem of long-distance wireless communication in such scenes can become a limiting factor, especially when automating the navigation of a UAV swarm. In this spirit, this work proposes an exploration strategy that enables UAVs, both individually and in small swarms, to quickly explore complex scenes in a decentralized fashion. By providing the decision-making capabilities to each UAV to switch between different execution modes, the proposed strategy strikes a great balance between cautious exploration of yet completely unknown regions and more aggressive exploration of smaller areas of unknown space. This results in full coverage of forest areas of variable density, consistently faster than the state of the art. Demonstrating successful deployment with a single UAV as well as a swarm of up to three UAVs, this work sets out the basic principles for multi-root exploration of cluttered scenes, with up to 65% speed up in the single UAV case and 40% increase in explored area for the same mission time in multi-UAV setups.