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On modern field-programmable gate arrays (FPGAs), certain critical path portions of the designs might be prearranged into many multi-cell macros during synthesis. These movable macros with constraints of shape and resources lead to challenging mixed-size placement for FPGA designs which cannot be addressed by previous analytical placers. Moreover, general timing-driven placement algorithms are facing challenges when handling real-world application design and ultrascale FPGA architectures. In this work, we propose AMF-Placer 2.0, an open-source comprehensive timing-driven analytical mixed-size FPGA placer. It supports mixed-size placement of heterogeneous resources (e.g., LUT/FF/LUTRAM/MUX/CARRY/DSP/BRAM) on FPGA, with an interface to Xilinx Vivado. Standing upon the shoulders of AMF-Placer 1.0, AMFPlacer 2.0 is equipped with a series of new techniques for timing optimization, including a simple but effective timing model, placement-blockage-aware anchor insertion, WNS-aware timing-driven quadratic placement, and sector-guided detailed placement. Based on a set of the latest large open-source benchmarks from various domains for Xilinx Ultrascale FPGAs, experimental results indicate that critical path delays realized by AMF-Placer 2.0 are averagely 2.2% and 0.59% higher than those achieved by commercial tool Xilinx Vivavo 2020.2 and 2021.2 respectively. Meanwhile, the average runtime of placement procedure of AMF-Placer 2.0 is 14% and 8.5% higher than Xilinx Vivavo 2020.2 and 2021.2 respectively. Although limited by the absence of the exact timing model of the device, the information of design hierarchy and accurate routing feedback, AMF-Placer 2.0 is the first open-source FPGA placer which can handle the timingdriven mixed-size placement of practical complex designs with various FPGA resources and achieves the comparable quality to the latest commercial tools.