Annals of Applied Probability, (1995) 5, 1008-1024.
1991 Mathematics Subject Classification: 60J80
A general (Crump-Mode-Jagers) spatial branching process is considered. The asymptotic behaviour of the numbers present at time $t$ in sets of the form $[ta, \infty)$ is obtained. As a consequence it is shown that, if $B_t$ is the position of the rightmost person at time $t$, $B_t/t$ converges to a constant, which can be obtained from the individual reproduction law, almost surely on the survival set of the process. This generalizes the known discrete-time results.
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