In this work we extend the approach used in [5] to perform distributed {AFMC} model checking. The part of a system held in one computer is modeled as a Kripke structure with border states. Moreover, we use assumptions about the truth of a formula in each state. Each process then repeatedly execute a slight modification of a standard sequential algorithm and exchange its results with other processes. In the paper we define the {AFMC} semantics that cope with border states and assumptions, present the distributed algorithm and show the main ideas of the proof of its correctness. Complexity and experimental results are provided as well.