  We study the growth of genuine multipartite entanglement in random quantum
circuit models, which include random unitary circuit models and the random
Clifford circuit. We find that for the random Clifford circuit, the growth of
multipartite entanglement remains slower in comparison to the random unitary
case. However, the final saturation value of multipartite entanglement is
almost the same in both cases. The behavior is then compared to the genuine
multipartite entanglement obtained in random matrix product states with a
moderately high bond dimension. We then relate the behavior of multipartite
entanglement to other global properties of the system, viz. the delocalization
of the many-body wavefunctions in Hilbert space. Along with this, we analyze
the robustness of such highly entangled quantum states obtained through random
unitary dynamics under weak measurements.

Quantum Physics;Statistical Mechanics;Strongly Correlated Electrons