transparency from alpha channel in texture doesn't show?

Ok, so I'm making progress and create my shader/material and textures,
loading a .png or targa files which are 32-bit deep, carrying a
picture a tree with the transparency mask in alpha, and the previewer
shows the alpha in action as expected when seldcting UseApha - all so
far so good..... but it doesn't show transparent when rendering. 

I have gone through the render settings over and over, there's no
parameters to say whether transparency should be used or not as found
in textures.

Is it not able to do so in the default Blender renderer?