  Binary rooted trees, both in the ordered and in the un-ordered case, are well
studied structures in the field of combinatorics. The aim of this work is to
study particular patterns in these classes of trees. We consider completely
unbalanced subtrees, where unbalancing is measured according to the so-called
Colless's index. The size of the biggest unbalanced subtree becomes then a new
parameter with respect to which we find several enumerations.
