Application of a thermally and/or electrically conductive compound to fill a thermal and/or EMI shielding gap between a first and a second surface. A supply of a fluent, form-stable compound is provided as an admixture of a cured polymer gel component, and a particulate filler component. An of the compound is dispensed from a nozzle or other orifice under an applied pressure onto one of the surfaces which, when opposed, form the gap, or into the gap formed between the surfaces. The gap is at least partially filled by at least a portion of the dispensed compound.