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This paper utilizes the family of affine projection algorithms (APAs) for distributed estimation in the adaptive diffusion networks. The diffusion APA (DAPA), the diffusion selective partial update (SPU) APA (DSPU-APA), the diffusion selective regressor (SR) APA (DSR-APA), and the diffusion dynamic selection (DS) APA (DDS-APA) are introduced in a unified way. In DSPU-APA, the weight coefficients are partially updated at each node during the adaptation. Therefore, the DSPU-APA has lower computational complexity in comparison to the DAPA. In addition, the convergence speed of the DSPU-APA is close to the DAPA. In DSR-APA, a subset of input regressors is optimally selected at each node during the adaptation. The dynamic selection of input regressors is performed in the DDS-APA. These strategies improve the performance of the conventional DAPA in terms of the steady-state error and computational complexity features. Also, by combining these algorithms, the DSPU-SR-APA and the DSPU-DS-APA are established, which are computationally efficient. The mean-square performance of the proposed algorithms is analyzed in the nonstationary environment and the generic relations for the theoretical learning curve and the steady-state error are derived. The analysis is based on the spatial-temporal energy conservation relation. The validity of the theoretical results and the good performance of the introduced algorithms are demonstrated by several computer simulations in diffusion networks.