Process model comprehension is essential for a variety of technical and managerial tasks. To facilitate comprehension, process models are often divided into subprocesses when they reach a certain size. However, depending on the task type this can either support or impede comprehension. To investigate this hypothesis, we conduct a comprehensive eye-tracking study, where we test two different types of comprehension tasks. These are local tasks focusing on a single subprocess, thereby benefiting from abstraction (i.e., irrelevant information is hidden), and global tasks comprising multiple subprocesses, thereby also benefiting from abstraction but impeded by fragmentation (i.e., relevant information is distributed across multiple fragments). Our subsequent analysis at task (coarse-grained) and phase (fine-grained) levels confirms the opposing effects of abstraction and fragmentation. For global tasks, we observe lower task comprehension, higher cognitive load, as well as more complex search and inference behaviors, when compared to local ones. An additional qualitative analysis of search and inference phases, based on process maps and time series, provides additional insights into the evolution of information processing and confirms the differences between the two task types. The fine-grained analysis at the phase level is based on a novel research method, allowing to clearly separate information search from information inference. We provide an extensive validation of this research method. The outcome of this work provides a more thorough understanding of the effects of fragmentation, in the context of modularized process models, at a coarse-grained level as well as at a fine-grained level, allowing for the development of task- and user-centric support, and opening up future research opportunities to further investigate information processing during process comprehension.