  We introduce the notion of extremal basis of tangent vector fields at a
boundary point of finite type of a pseudo-convex domain in $\mathbb{C}^n$. Then
we define the class of geometrically separated domains at a boundary point, and
give a description of their complex geometry. Examples of such domains are
given, for instance, by locally lineally convex domains, domains with locally
diagonalizable Levi form, and domains for which the Levi form have comparable
eigenvalues at a point. Moreover we show that these domains are localizable.
Then we define the notion of "adapted pluri-subharmonic function" to these
domains, and we give sufficient conditions for his existence. Then we show that
all the sharp estimates for the Bergman ans Szeg\"o projections are valid in
this case. Finally we apply these results to the examples to get global and
local sharp estimates, improving, for examlple, a result of Fefferman, Kohn and
Machedon on the Szeg\"o projection.
