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In this paper we produce infinite families of counterexamples to Jantzen'squestion posed in 1980 on the existence of Weyl $p$-filtrations for Weylmodules for an algebraic group and Donkin's Tilting Module Conjectureformulated in 1990. New techniques to exhibit explicit examples are providedalong with methods to produce counterexamples in large rank fromcounterexamples in small rank. Counterexamples can be produced via our methodsfor all groups other than when the root system is of type $\rm{A}_{n}$ or$\rm{B}_{2}$.

On Donkin's Tilting Module Conjecture II: Counterexamples