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 1280x720, 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 (30x 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. Code and dataset are released at https://github.com/boomluo02/EEMFlowPlus.