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Our aim in this work is to study exact Osserman limit linear series on curvesof compact type $X$ with three irreducible components. This case is quitedifferent from the case of two irreducible components studied by Osserman. Forinstance, for curves of compact type with two irreducible components, everyrefined Eisenbud-Harris limit linear series has a unique exact extension. But,for the case of three irreducible components, this property is no longer true.We find a condition characterizing when a given refined Eisenbud-Harris limitlinear series has a unique exact extension. To do this, it is necessary tounderstand how to construct exact extensions. We find a constructive method,which describes how to construct all exact extensions of refined limit linearseries. By our method, we get that every refined limit linear series has atleast one exact extension.

Limit linear series for curves of compact type with three irreducible components