Replacing Large Textures with Smaller Ones

I'd like to see if I can downsize the textures at my place for faster loading for my guests. If I delete the existing texture file from my inventory and upload a smaller one with the same name, will it automatically replace it for everyone? Or will it get assigned a new secret special number by the LL servers necessitating reapplying it to every surface? Or does the texture currently in use actually reside in the object it's texturing?

I'm trying to find the most efficient way of doing this as I'll be making a few dozen changes and I'd rather spend my time playing

You'll have to re-apply the new texture to each surface. Every asset in SL has a unique universal identifier, which is completely separate from its name. You could have a thousand textures all with the same name, and they'd all be completely unique assets.

Unfortunately, SL does not keep track of any procedural construction history for objects. There's no way to tell the database "okay, break the connection to this node over here, and reassign it to that one over there", like you could in offline 3D modeling apps like Maya. We just don't have that level of back end access.

Thanks for the info. I was afraid of that but wanted to check before I spent the time doing it.

Now I'll go spend the time doing it....