Abstract For any fixed integer $d\geq 2$, the $d$ary increasing tree is a rooted, ordered, labeled tree where the outdegree is bounded by $d$,
and the labels along each path beginning at the root increase. Total path length, or search cost, for a rooted tree is defined as the sum of all
roottonode distances and the Sackin index is defined as the sum of the depths of its leaves.
We study these quantities in random $d$ary increasing trees.
