Performance and scalability of model transformations are becoming prominent topics in Model-Driven Engineering. In previous work, we introduced LinTra, a platform for executing out-place model transformations in parallel. LinTra is based on the Linda coordination language for archiving concurrency and distribution and is intended to be used as a middleware where high-level model transformation languages (such as ATL and QVT) are compiled. To define modularly the compilation, this paper presents a minimal, yet sufficient, collection of primitive operators that can be composed to (re-)construct any out place, unidirectional model transformation language (MTL). These primitives enable any MTL to be executed in parallel in a transparent way, without altering the original transformation.