This is related to my previous Travelling Attribute Wave post but it's getting a bit long and complicated so I thought it's better as a separate post.

I've got an object with a VOPSOP network and would like to move points along their normals (so that parts of the object could be shrunk or expanded according to the value of an attribute).

Do I need to create these normals first? In VOPSOPs, is the Global Variable P always in world space?

First, the Peak SOP allows you to move points along normals.

As for VOPs, P is in the same space as your SOP network.
N, your point normal, is a global that you have access to.

To move a point along the normal its simply, P = P+N*scaling_factor.

Where scaling factor can be some attribute on the surface.

Thanks. Some of the tutorials say something along the lines of “there's no normals by default so lets create some with the point SOP”, so I was little confused as to wether I have to tell Houdini…blabla…

Anyway, great!

Nah, if normals don't exist Houdini creates them for you then gets rid of them once you are done.