  The global persistence exponent $\theta_g$ is calculated for the
two-dimensional Blume-Capel model following a quench to the critical point from
both disordered states and such with small initial magnetizations.
  Estimates are obtained for the nonequilibrium critical dynamics on the
critical line and at the tricritical point.
  Ising-like universality is observed along the critical line and a different
value $\theta_g =1.080(4)$ is found at the tricritical point.
