  We introduce the problem of isolating several nodes in random recursive trees
by successively removing random edges, and study the number of random cuts that
are necessary for the isolation. In particular, we analyze the number of random
cuts required to isolate $\ell$ selected nodes in a size-n random recursive
tree for three different selection rules, namely (i) isolating all of the nodes
labelled 1,2,...,$\ell$ (thus nodes located close to the root of the tree),
(ii) isolating all of the nodes labelled n+1-$\ell$,n+2-$\ell$,...,n (thus
nodes located at the fringe of the tree), and (iii) isolating $\ell$ nodes in
the tree, which are selected at random before starting the edge-removal
procedure. Using a generating functions approach we determine for these
selection rules the limiting distribution behavior of the number of cuts to
isolate all selected nodes, for $\ell$ fixed and n tending to infinity.
