  Both the deterministic and stochastic sandpile models are studied on the
percolation backbone, a random fractal, generated on a square lattice in
$2$-dimensions. In spite of the underline random structure of the backbone, the
deterministic Bak Tang Wiesenfeld (BTW) model preserves its positive time
auto-correlation and multifractal behaviour due to its complete toppling
balance, whereas the critical properties of the stochastic sandpile model (SSM)
still exhibits finite size scaling (FSS) as it exhibits on the regular
lattices. Analysing the topography of the avalanches, various scaling relations
are developed. While for the SSM, the extended set of critical exponents
obtained is found to obey various the scaling relation in terms of the fractal
dimension $d_f^B$ of the backbone, whereas the deterministic BTW model, on the
other hand, does not. As the critical exponents of the SSM defined on the
backbone are related to $d_f^B$, the backbone fractal dimension, they are found
to be entirely different from those of the SSM defined on the regular lattice
as well as on other deterministic fractals. The SSM on the percolation backbone
is found to obey FSS but belongs to a new stochastic universality class.
