  We study two models of correlated bond- and site-disorder on the kagome
lattice considering both translationally invariant and completely disordered
systems. The models are shown to exhibit a perfectly flat ground state band in
the presence of disorder for which we provide exact analytic solutions. Whereas
in one model the flat band remains gapped and touches the dispersive band, the
other model has a finite gap, demonstrating that the band touching is not
protected by topology alone. Our model also displays fully saturated
ferromagnetic groundstates in the presence of repulsive interactions, an
example of disordered flat band ferromagnetism.
