Vitrimers are covalent network materials, comparable in structure to classical thermosets. Unlike normal thermosets, they possess a chemical bond swap mechanism that makes their structure dynamic and suitable for activated welding and even autonomous self-healing. The central question in designing such materials is the trade-off between autonomy and material stability: The swap mechanism facilitates the healing but it also facilitates creep, which makes the perfectly stable self-healing solid a hard goal to reach. Here, we address this question for the case of self-healing vitrimers made from star polymers. Using coarse-grained molecular dynamics simulations, we study the adhesion of two vitrimer samples and find that they bond together on timescales that are much shorter than the stress relaxation time. We show that the swap mechanism allows the star polymers to diffuse through the material through coordinated swap events, but the healing process is much faster and does not depend on this mobility.