A multi-type critical emigration branching process

A multi-type age-dependent Bellman-Harris process is defined such that each cell is subject to emigration in accord with a simple renewal process, independent of other cells, with the renewal process depending only on its type. This age-dependent emigration process may be made to act similar to critical multi-type Bellman-Harris branching process. Limit theorems analogous to those for critical multi-type Bellman-Harris processes are given. A multi-type critical emigration-immigration model is also considered.