Proportional-type algorithms have attracted much attention because of their fast convergence ability for sparse system identification. To overcome the drawbacks of existing block proportional methods stemming from inadequate block partitioning, this article develops tap-amplitude-based block partitioning methods. In the procedure, we present two block proportional normalized least-mean-square (PNLMS) algorithms named (i) ABx-PNLMS and (ii) ABy-PNLMS. In the first algorithm, the proportional gain depends on the rank-based tap-weight block on the x-axis. In comparison, the second algorithm determines the proportional gain by dynamically partitioning the y-axis in a non-uniform manner. Nevertheless, both algorithms have a common feature, namely, weights of similar magnitude are grouped together. By further incorporating an adaptive decorrelation mechanism into the ABx-PNLMS and ABy-PNLMS, two improved decorrelation proportional alogrithms are developed to speed up the convergence for colored inputs. Computer simulation results on system identification and acoustic echo cancellation demonstrate the effectiveness of the proposed approaches.