  The two-dimensional comb lattice $C_2$ is a natural spanning tree of the
Euclidean lattice $\mathbb{Z}^2$. We study three related cluster growth models
on $C_2$: internal diffusion limited aggregation (IDLA), in which random
walkers move on the vertices of $C_2$ until reaching an unoccupied site where
they stop; rotor-router aggregation in which particles perform deterministic
walks, and stop when reaching a site previously unoccupied; and the divisible
sandpile model where at each vertex there is a pile of sand, for which, at each
step, the mass exceeding 1 is distributed equally among the neighbours. We
describe the shape of the divisible sandpile cluster on $C_2$, which is then
used to give inner bounds for IDLA and rotor-router aggregation.
