Abstract: If X is a positive random variable with a finite mean then the probability distribution with density proportional to X is called its size biased version. For Markov chains admitting a positive eigen function one can construct a size biased version of this chain which is also Markov.. In this talk we derive conditions for the two chains to be dominated by each other over the full trajectory space.. We then apply this to derive a LLOGL result for supercritical branching processes with arbitrary type space.