2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156395A structural condition is given for finite maximal antichains in the homomorphism order of relational structures to have the splitting property. It turns out that non-splitting antichains appear only at the bottom of the order. Moreover, we examine looseness and finite antichain extension property for some subclasses of the homomorphism poset. Finally, we take a look at cut-points in this order.10 pagesCombinatorics06D05;05C15text