  We discuss the local and nonlocal dissipation effects on the existence of the
global phase coherence transitions in two dimensional Josephson-coupled
junctions. The quantum phase transitions are also examined for various lattice
geometries: square, triangular and honeycomb. The T=0 superconductor-insulator
phase transition is analyzed as a function of several control parameters which
include self-capacitance and junction capacitance and both local and nonlocal
dissipation effects. We found the critical value of the nonlocal dissipation
parameter \alpha_{1} depends on a geometry of the lattice. The critical value
of the normal state conductance seems to be difficult to obtain experimentally
if we take into consideration different damping mechanisms which are presented
in real physical systems.
