A turbine rotor blade for a turbine section of an engine, the turbine rotor blade comprising: a platform; and an airfoil extending from the platform into a mainstream gas path of the turbine section, the airfoil comprising a first side wall; a second side wall joined to the first side wall at a leading edge and a trailing edge; a tip cap extending between the first side wall and the second side wall; a first parapet wall extending from the first side wall, wherein the first parapet wall is defined by a first radial surface on a first side facing the tip cap a tip edge, and an exterior surface on a second side opposite the tip cap; a first cooling hole (400, 700) that extends through the tip cap, through a step, the first parapet wall and the tip edge configured to deliver cooling air having a closed channel section (466, 766) that extends through the step and the tip cap, and an open channel section (464, 764) that extends through the outer radial section to the step through the first radial surface of the first parapet wall, the open channel section (464, 764) forming a slot, wherein the open channel section is open relative to the first radial surface; and the step extending in a chordwise direction and formed between the first radial surface of the first parapet wall and the tip cap, the step having a radial surface and an axial surface, characterized in that the first cooling hole transitions from the closed channel section to the open channel section at a distance from the axial surface such that the closed channel section has an outlet at the distance from the axial surface of the step. a platform; and an airfoil extending from the platform into a mainstream gas path of the turbine section, the airfoil comprising a first side wall; a second side wall joined to the first side wall at a leading edge and a trailing edge; a tip cap extending between the first side wall and the second side wall; a first parapet wall extending from the first side wall, wherein the first parapet wall is defined by a first radial surface on a first side facing the tip cap a tip edge, and an exterior surface on a second side opposite the tip cap; a first cooling hole (400, 700) that extends through the tip cap, through a step, the first parapet wall and the tip edge configured to deliver cooling air having a closed channel section (466, 766) that extends through the step and the tip cap, and an open channel section (464, 764) that extends through the outer radial section to the step through the first radial surface of the first parapet wall, the open channel section (464, 764) forming a slot, wherein the open channel section is open relative to the first radial surface; and the step extending in a chordwise direction and formed between the first radial surface of the first parapet wall and the tip cap, the step having a radial surface and an axial surface, characterized in that the first cooling hole transitions from the closed channel section to the open channel section at a distance from the axial surface such that the closed channel section has an outlet at the distance from the axial surface of the step. a first side wall; a second side wall joined to the first side wall at a leading edge and a trailing edge; a tip cap extending between the first side wall and the second side wall; a first parapet wall extending from the first side wall, wherein the first parapet wall is defined by a first radial surface on a first side facing the tip cap a tip edge, and an exterior surface on a second side opposite the tip cap; a first cooling hole (400, 700) that extends through the tip cap, through a step, the first parapet wall and the tip edge configured to deliver cooling air having a closed channel section (466, 766) that extends through the step and the tip cap, and an open channel section (464, 764) that extends through the outer radial section to the step through the first radial surface of the first parapet wall, the open channel section (464, 764) forming a slot, wherein the open channel section is open relative to the first radial surface; and the step extending in a chordwise direction and formed between the first radial surface of the first parapet wall and the tip cap, the step having a radial surface and an axial surface, characterized in that the first cooling hole transitions from the closed channel section to the open channel section at a distance from the axial surface such that the closed channel section has an outlet at the distance from the axial surface of the step.