2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/162852Higher-rank graph generalisations of the Popescu-Poisson transform are constructed, allowing us to develop a dilation theory for higher rank operator tuples. These dilations are joint dilations of the families of operators satisfying relations encoded by the graph structure which we call $Λ$-contractions or $Λ$-coisometries. Besides commutant lifting results and characterisations of pure states on higher rank graph algebras several applications to the structure theory of non-selfadjoint graph operator algebras are presented generalising recent results in special cases.25 pages; v3 corrects a definition of a doubly commuting $Λ$-contraction and adds a reference. The paper will appear in the Journal of Operator TheoryOperator AlgebrasFunctional Analysis47A20 (Primary); 05C20, 46L05, 47A13, 47L75 (Secondary)text