Simple extensions of limit linear series for curves of compact type with three irreducible components

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 find a method, which describes how to construct all simple extensions of refined Eisenbud–Harris limit linear series. Also, we get that every refined limit linear series has at least one simple extension. Given such a simple extension, we find the multidegrees which determine all simple bases.