In this paper, we explore the problem of event-based meshflow estimation, a novel task that involves predicting a spatially smooth sparse motion field from event cameras. To start, we review the state-of-the-art in event-based flow estimation, highlighting two key areas for further research: i) the lack of meshflow-specific event datasets and methods, and ii) the underexplored challenge of event data density. First, we generate a large-scale High-Resolution Event Meshflow (HREM) dataset, which showcases its superiority by encompassing the merits of high resolution at 1280 × 720, handling dynamic objects and complex motion patterns, and offering both optical flow and meshflow labels. These aspects have not been fully explored in previous works. Besides, we propose Efficient Event-based MeshFlow (EEMFlow) network, a lightweight model featuring a specially crafted encoder-decoder architecture to facilitate swift and accurate meshflow estimation. Furthermore, we upgrade EEMFlow network to support dense event optical flow, in which a Confidence-induced Detail Completion (CDC) module is proposed to preserve sharp motion boundaries. We conduct comprehensive experiments to show the exceptional performance and runtime efficiency (30×faster) of our EEMFlow model compared to the recent state-of-the-art flow method. As an extension, we expand HREM into HREM+, a multi-density event dataset contributing to a thorough study of the robustness of existing methods across data with varying densities, and propose an Adaptive Density Module (ADM) to adjust the density of input event data to a more optimal range, enhancing the model’s generalization ability. We empirically demonstrate that ADM helps to significantly improve the performance of EEMFlow and EEMFlow+ by 8% and 10%, respectively.