A variable-nozzle turbine cartridge for a variable-nozzle turbine, the cartridge comprising an assembly of: a generally annular nozzle ring and an array of vanes circumferentially spaced about the nozzle ring, each vane being rotatably mounted to the nozzle ring and connected to a rotatable actuator ring such that rotation of the actuator ring rotates the vanes for regulating exhaust gas flow therethrough; an insert having a tubular portion configured for being sealingly received into a bore of a turbine housing and having a nozzle portion extending generally radially out from one end of the tubular portion, the nozzle portion being axially spaced from the nozzle ring such that the vanes extend between the nozzle ring and the nozzle portion; and a plurality of spacers connected between the nozzle portion of the insert and the nozzle ring for securing the nozzle ring to the insert and maintaining an axial spacing between the nozzle portion of the insert and the nozzle ring; wherein each of the spacers comprises a two-piece self-centering assembly comprising a tubular sleeve and a pin, each sleeve defining a through-passage and each corresponding pin passing through the through-passage, each pin having a first end portion that projects from a first end of the sleeve and passes through an aperture defined by the nozzle ring and having a second end portion that projects from an opposite second end of the sleeve and passes through an aperture defined in the nozzle portion of the insert, the first end of each pin being secured to the nozzle ring and the second end of each pin being secured to the nozzle portion of the insert; wherein the pins are secured to the nozzle ring and the nozzle portion so as to draw the nozzle ring and the nozzle portion axially toward each other so that the first ends of the sleeves bear against a face of the nozzle ring and the second ends of the sleeves bear against a face of the nozzle portion, the sleeves keeping the nozzle ring and the nozzle portion spaced apart, and wherein one of the first and second ends of each sleeve forms a conical surface that is coaxial with the through-passage of the sleeve, and the face against which the one end of each sleeve bears defines a corresponding conical countersink that is coaxial with the aperture through which the end portion of the pin passes, such that engagement between the conical surfaces of the sleeves and the conical countersinks maintains the through-passages of the sleeves coaxial with the apertures for the pins, whereby the self-centering assemblies maintain the sleeves substantially coaxial with the corresponding pins. a generally annular nozzle ring and an array of vanes circumferentially spaced about the nozzle ring, each vane being rotatably mounted to the nozzle ring and connected to a rotatable actuator ring such that rotation of the actuator ring rotates the vanes for regulating exhaust gas flow therethrough; an insert having a tubular portion configured for being sealingly received into a bore of a turbine housing and having a nozzle portion extending generally radially out from one end of the tubular portion, the nozzle portion being axially spaced from the nozzle ring such that the vanes extend between the nozzle ring and the nozzle portion; and a plurality of spacers connected between the nozzle portion of the insert and the nozzle ring for securing the nozzle ring to the insert and maintaining an axial spacing between the nozzle portion of the insert and the nozzle ring; wherein each of the spacers comprises a two-piece self-centering assembly comprising a tubular sleeve and a pin, each sleeve defining a through-passage and each corresponding pin passing through the through-passage, each pin having a first end portion that projects from a first end of the sleeve and passes through an aperture defined by the nozzle ring and having a second end portion that projects from an opposite second end of the sleeve and passes through an aperture defined in the nozzle portion of the insert, the first end of each pin being secured to the nozzle ring and the second end of each pin being secured to the nozzle portion of the insert; wherein the pins are secured to the nozzle ring and the nozzle portion so as to draw the nozzle ring and the nozzle portion axially toward each other so that the first ends of the sleeves bear against a face of the nozzle ring and the second ends of the sleeves bear against a face of the nozzle portion, the sleeves keeping the nozzle ring and the nozzle portion spaced apart, and wherein one of the first and second ends of each sleeve forms a conical surface that is coaxial with the through-passage of the sleeve, and the face against which the one end of each sleeve bears defines a corresponding conical countersink that is coaxial with the aperture through which the end portion of the pin passes, such that engagement between the conical surfaces of the sleeves and the conical countersinks maintains the through-passages of the sleeves coaxial with the apertures for the pins, whereby the self-centering assemblies maintain the sleeves substantially coaxial with the corresponding pins.