How do I properly lay a tongue and groove plywood subfloor in a remodel?
You defiantly need to support the subfloor around the perimeter.
Let's say this is your floor without plywood.

You want to put plywood down, but the edge of the sheet has nothing under it for support.

If you don't support the plywood, you'll end up with a &quot;soft&quot; spot around the perimeter.  Stepping, or adding weight to this area will cause the plywood to flex. This flexing will cause the area to feel spongy, and could damage the flooring (depending on the type of flooring). To solve this problem, you have a couple options.
Blocking.
Installing blocking perpendicular to the joists will support the edge of the sheet.


The size and spacing of the blocking will be determined by local codes, so consult your local government for these requirements.
Additional Joist
Another option, is to install an additional joist to support the edge of the sheet.


This extra joist may not have to span the entire length, and may be able to be supported by blocking between the existing joists. Again, check with local building codes to determine what is required.