a straight seat post is 7/8" at the top. the rest depends on the seat tube ID its going in on the bike frame.

you buy a saddle clip to fit on top of them, to mount the saddle..

Kalloy makes those in most-all diameters .. low cost..

start adding an integrated saddle rail mount, and the range starts at Zero.. it sits directly on top.
Thomson is one of that type, to have a setback from directly on top they bend the post shaft.

others design the head so the clamp mech is behind the seatpost centerline.. including Kalloy.