Visually-situated text parsing (VsTP) has recently seen notable advancements, driven by the growing demand for automated document understanding and the emergence of large language models capable of processing document-based questions. While various methods have been proposed to tackle the complexities of VsTP, existing solutions often rely on task-specific architectures and objectives for individual tasks. This leads to modal isolation and complex workflows due to the diversified targets and heterogeneous schemas. In this paper, we introduce OmniParser V2, a universal model that unifies VsTP typical tasks, including text spotting, key information extraction, table recognition, and layout analysis, into a unified framework. Central to our approach is the proposed Structured-Points-of-Thought (SPOT) prompting schemas, which improves model performance across diverse scenarios by leveraging a unified encoder-decoder architecture, objective, and input\&output representation. SPOT eliminates the need for task-specific architectures and loss functions, significantly simplifying the processing pipeline. Our extensive evaluations across four tasks on eight different datasets show that OmniParser V2 achieves state-of-the-art or competitive results in VsTP. Additionally, we explore the integration of SPOT within a multimodal large language model structure, further enhancing visual text parsing capabilities on four tasks, thereby confirming the generality of SPOT prompting technique. The code is available at \href{https://github.com/AlibabaResearch/AdvancedLiterateMachinery}{AdvancedLiterateMachinery}.