Efficient thermal management of large vertically stacked integrated circuits (ICs) requires a material with high thermal conductivity inside the micrometer-sized gaps between the IC dies. Such an underfill material can be obtained by adding thermally conductive filler particles at high loadings to the adhesive matrix material. However, viscosity requirements for the state-of-the-art capillary-driven filling of particle-loaded adhesives limit the particle fill fraction to values lower than those necessary to reach true percolation. Accordingly, heat transfer through the composite material is dominated by conduction through the adhesive matrix material. We propose using an alternative, sequential filling method to achieve percolation with particles down to 1μm in diameter. The percolating thermal underfill (PTU) can be achieved by a centrifuge-assisted filling of micrometer-sized particles, followed by a backfilling of a low-viscosity epoxy with long open time acting as matrix material, and a final thermal curing step. In this paper, we present and discuss the fabrication and relevant process parameters of the PTU composite material in chip stacks with critical dimensions below 30μm. The wet dispensing of alumina particles with a diameter distribution of 1- 15μm is proposed for overcoming the agglomeration observed for dry particle filling. Thermal conductivities of up to 3 W/(mK) for the underfill system with a particle fill fraction of 61% were achieved, which is three times higher than those of commercially available capillary thermal underfills. Critical parameters in the formation of the percolating composite, such as the choice of filler material and its refinement, as well as the properties of the particle bed and the process parameters for the centrifugal filling, epoxy capillary backfilling, and composite curing are addressed.