%0 Journal Article %T On typical leaves of a measured foliated 2-complex of thin type %A Ivan Dynnikov %A Alexandra Skripchenko %J Mathematics %D 2013 %I arXiv %X It is known that all but finitely many leaves of a measured foliated 2-complex of thin type are quasi-isometric to an infinite tree with at most two topological ends. We show that if the foliation is cooriented, and the associated R-tree is self-similar, then a typical leaf has exactly one topological end. We also construct the first example of a foliated 2-complex of thin type whose typical leaf has exactly two topological ends. `Typical' means that the property holds with probability one in a natural sense. %U http://arxiv.org/abs/1309.4884v1