  We investigate centrality and root-inference properties in a class of growing
random graphs known as sublinear preferential attachment trees. We show that a
continuous time branching processes called the Crump-Mode-Jagers (CMJ)
branching process is well-suited to analyze such random trees, and prove that
almost surely, a unique terminal tree centroid emerges, having the property
that it becomes more central than any other fixed vertex in the limit of the
random growth process. Our result generalizes and extends previous work
establishing persistent centrality in uniform and linear preferential
attachment trees. We also show that centrality may be utilized to generate a
finite-sized $1-\epsilon$ confidence set for the root node, for any $\epsilon >
0$ in a certain subclass of sublinear preferential attachment trees.
