3d plots of z functions regions of conversion

(1) I have a 3D plot of functions in z-complex space exptending from the origen to same convenient radius ρ1 greater than unity.
(2) Need a second 3D plot of of the same functions extending from some radius ρ2<ρ1 outwardly.
(3) The 3D plot may contain poles and zeros
(4) The xy imprint is circular with a hole centered at the origen.
(4) I have tried meshgrid and other tools to no avail.
(5) Can someone suggest the steps necesssary to obtain the desired result? Thanks