  We study the distribution of the maximal jump of continuous-state branching
processes. Several exact expressions and explicit asymptotics of both the local
maximal jump and the global maximal jump are obtained. We also compare the
distribution of the maximal jump and the L\'{e}vy measure to get several
absolute continuity results. Then we study local convergence of
continuous-state branching processes under various conditionings. We obtain
complete results under the conditioning of large maximal jump, and partial
results under two other conditionings, which are, the conditioning of large
width, and, the conditioning of large total mass.
