We study simple Osserman limit linear series (that is, Osserman limit linear series having a simple basis) on curves of compact type with three irreducible components. For compact type curves with two components, every exact limit linear series is simple. But, for the case of three components, this property is no longer true. We study a certain distributivity property related with the existence of a simple basis and we find characterizations of that property at any fixed multidegree. Also, we find a characterization of simple limit linear series among the exact limit linear series. In our approach, we also study other structure similar to a simple basis and we get a certain inequality for any exact limit linear series.