We use a numerical implementation of the strong disorder renormalizationgroup (RG) method to study the low-energy fixed points of random Heisenberg andtight-binding models on different types of fractal lattices. For the Heisenbergmodel new types of infinite disorder and strong disorder fixed points arefound. For the tight-binding model we add an orbital magnetic field and useboth diagonal and off-diagonal disorder. For this model besides the gap spectrawe study also the fraction of frozen sites, the correlation function, thepersistent current and the two-terminal current. The lattices with an evennumber of sites around each elementary plaquette show a dominant $\phi_0=h/e$periodicity. The lattices with an odd number of sites around each elementaryplaquette show a dominant $\phi_0/2$ periodicity at vanishing diagonaldisorder, with a positive weak localization-like magnetoconductance at infinitedisorder fixed points. The magnetoconductance with both diagonal andoff-diagonal disorder depends on the symmetry of the distribution of on-siteenergies.

Strong disorder renormalization group on fractal lattices: Heisenberg models and magnetoresistive effects in tight binding models