On Slupecki classes in the systems $P_k\times\dots\times P_l$

We describe all $2^m-1$ precomplete Slupecki classes in systems of the form $P_{k_1}\times \dots\times P_{k_m}$. We prove that any minimal relation defining a precomplete class in the system $P_{k_1}\times\dots\times P_{k_m}$ is either one-based, or a multibased completely reflexive and completely symmetric relation.