Process models support a variety of tasks, which can be organized differently. Notably one can discern local tasks focusing on a single part of a model and global tasks requiring an overview of several parts. These two task types are assumed to affect users’ understanding of processes differently especially if the processes are decomposed into many interlinked and self-contained models through modularization. Local tasks can benefit from abstraction as they enable information hiding, while global tasks can be impeded by fragmentation caused by the split attention effect. Following a task-centric approach, we substantiate this hypothesis by investigating the cognitive effects of abstraction and fragmentation in modularization. Therein, we focus particularly on horizontal modularization and study users’ cognitive load, comprehension and behavior when solving local and global tasks. Our findings confirm that, compared to abstraction, fragmentation hinders users’ comprehension of the model and raises their cognitive load. Additionally, users exhibit different search and integration behaviors when performing local and global tasks. The outcome of this work motivates the shift from artifact-centric to task-centric empirical studies, raises the need for approaches to mitigate the effect of fragmentation and explores different alternatives to achieve this goal.