Extremely large antenna array (ELAA) is key to enhancing spectral efficiency in 6G networks. Leveraging the distributed nature of multi-unmanned aerial vehicle (UAV) systems enables the formation of distributed ELAA, which often operate in the near-field region with spatial sparsity, rendering the conventional far-field plane wave assumption invalid. This paper investigates channel estimation for distributed near-field multi-UAV communication systems. We first derive closed-form signal-to-noise ratio (SNR) expressions under the plane wave model (PWM), spherical wave model (SWM), and a hybrid spherical-plane wave model (HSPWM), also referred to as the cross-field model, within a distributed uniform planar array (UPA) scenario. The analysis shows that HSPWM achieves a good balance between modeling accuracy and analytical tractability. Based on this, we propose two channel estimation algorithms: the spherical-domain orthogonal matching pursuit (SD-OMP) and the tensor-OMP. The SD-OMP generalizes the polar domain to jointly consider elevation, azimuth, and range. Under the HSPWM, the channel is naturally formulated as a tensor, enabling the use of tensor-OMP. Simulation results demonstrate that tensor-OMP achieves normalized mean square error (NMSE) performance comparable to SD-OMP, while offering reduced computational complexity and improved scalability.