Large deviation results are obtained for the normed limit of a supercritical multi-type branching process. Starting from a single individual of type i, let L[i] be the normed limit of the branching process, and let Z k [i] be the minimum possible population size at generation k. If Z k [i] is bounded in k (bounded minimum growth) then we show that P(L[i] ≤ x) = P(L[i] = 0) + xF ∗[i](x) + o(x) as x → 0. If Z k [i] grows exponentially in k (exponential minimum growth) then we show that − log P(L… CONTINUE READING