There are several way to copy surfaces depending on dependecy and relationship.
1) Genereate a step file using surface only and import to new part.
2) Remove any surfaces that you don't need. (This is best when you don't want relationships).
3) Note:(At this time you can also copy and paste but it will cause dependecies)
1) Copy the surfaces on the model and paste.
2) Open up all ref
3) copy the feature (paste) from one model part to the other.
1) Export the curves only and re-import - Then re-create surfaces in the model.
Good luck - More options are more complex. (Style - re-create in asm mode).
Thanks & Regards
Mechanical ENGR STF PRNCPL
Advanced Data Capture
Motorola Solutions, Inc.