  We study the nature of tunneling phase time for various quantum mechanical
structures such as networks and rings having potential barriers in their arms.
We find the generic presence of Hartman effect, with superluminal velocities as
a consequence, in these systems. In quantum networks it is possible to control
the `super arrival' time in one of the arms by changing the parameters on
another arm which is spatially separated from it. This is yet another quantum
nonlocal effect. Negative time delays (time advancement) and `ultra Hartman
effect' with negative saturation times have been observed in some parameter
regimes. In presence and absence of Aharonov-Bohm (AB) flux quantum rings show
Hartman effect. We obtain the analytical expression for the saturated phase
time. In the opaque barrier regime this is independent of even the AB flux
thereby generalizing the Hartman effect. We also briefly discuss the concept of
"space collapse or space destroyer" by introducing a free space in between two
barriers covering the ring. Further we show in presence of absorption the
reflection phase time exhibits Hartman effect in contrast to the transmission
phase time.
