The zero-temperature Glauber dynamics is used to investigate the persistence probability $P(t)$ in the Potts model with $Q=3,4,5,7,9,12,24,64, 128$, $256, 512, 1024,4096,16384 $,..., $2^{30}$ states on {it directed} and {it undirected} Barabasi-Albert networks and Erdos-Renyi random graphs. In this model it is found that $P(t)$ decays exponentially to zero in short times for {it directed} and {it undirected} Erdos-Renyi random graphs. For {it directed} and {it undirected} Barabasi-Albert networks, in contrast it decays exponentially to a constant value for long times, i.e, $P(infty)$ is different from zero for all $Q$ values (here studied) from $Q=3,4,5,..., 2^{30}$; this shows blocking for all these $Q$ values. Except that for $Q=2^{30}$ in the {it undirected} case $P(t)$ tends exponentially to zero; this could be just a finite-size effect since in the other blocking cases you may have only a few unchanged spins.
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