Parallel implementation of numerical adaptive mesh refinement (AMR)strategies for solving 3D elastostatic contact mechanics problems is an essential step toward complex simulations that exceed current performance levels. This paper introduces a scalable, robust, and efficient algorithm to deal with 2D and 3D elastostatics contact problems between deformable bodies in a finite element framework. The proposed solution combines a treatment of the contact problem by a node-to-node pairing algorithm with a penalization technique and a non-conforming h-adaptive refinement of quadrilateral/hexahedral meshes based on an estimate-mark-refine approach in a parallel framework. One of the special features of our parallel strategy is that contact paired nodes are hosted by the same MPI tasks, which reduces the number of exchanges between processes for building the contact operator. The mesh partitioning introduced in this paper respects this rule and is based on an equidistribution of elements over processes, without any other constraints. In order to preserve the domain curvature while hierarchical mesh refinement, super-parametric elements are used. This functionality enables the contact zone to be well detected during the AMR process, even for an initial coarse mesh and low-order discretization schemes. The efficiency of our contact-AMR-HPC strategy is assessed on 2D and 3D Hertzian contact problems. Different AMR detection criteria are considered. Various convergence analyses are conducted. Parallel performances up to 1024 cores are illustrated. Furthermore, memory footprint and preconditionners performance are analyzed.