We present a subordination theory for spatial branching processes. This theory is developed in three different settings, first for branching Markov processes, then for superprocesses and finally for the path-valued process called the {\it Brownian snake}. As a common feature of these three situations, subordination can be used to generate new branching mechanisms. As an application, we investigate the compact support property for superprocesses with a general branching mechanism.

MSC Classifications:

60J80, 60J25, 60J27, 60J55, 60G57 show english descriptions Branching processes (Galton-Watson, birth-and-death, etc.)
Continuous-time Markov processes on general state spaces
Continuous-time Markov processes on discrete state spaces
Local time and additive functionals
Random measures 60J80 - Branching processes (Galton-Watson, birth-and-death, etc.)
60J25 - Continuous-time Markov processes on general state spaces
60J27 - Continuous-time Markov processes on discrete state spaces
60J55 - Local time and additive functionals
60G57 - Random measures

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