The distribution of passenger demand over the transit network is forecasted using transit assignment models which conventionally assume that passenger loads satisfy network equilibrium conditions. The approach taken in this study is to model transit path choice as a within-day dynamic process influenced by network state variation and real-time information. The iterative network loading process leading to steady-state conditions is performed by means of day-to-day learning implemented in an agent-based simulation model. We explicitly account for adaptation and learning in relation to service uncertainty, on-board crowding and information provision in the context of congested transit networks. This study thus combines the underlying assignment principles that govern transit assignment models and the disaggregate demand modeling enabled by agent-based simulation modeling. The model is applied to a toy network for illustration purposes, followed by a demonstration for the rapid transit network of Stockholm, Sweden. A full-scale application of the proposed model shows the day-to-day travel time and crowding development for different levels of network saturation and when deploying different levels of information availability.