Dual Booting LL 2.0 with other Ubuntu (14.04) based distros

[gold_finger]

When I boot  LL 2.0, in either a dual- or multi-boot system (all Linux based), it mounts the partition or partitions (e.g. '40 GB Volume' shown below an icon of the drive) for the other OS or OS-es on the top left-hand side of the desktop screen.  With the system I have, both Zorin OS and Elementary OS, do not do this. Is there something I can do to prevent these automounting on the screen?

I don't think the other partitions are actually being mounted.  You are probably just seeing icons for them placed on the desktop.  If you double-click the icons, then they will be mounted.  If you open the file manager and look along left-hand side you will see those partitions listed, but you should notice that they are slightly grayed out -- meaning they are not mounted.  If you click them, then they will be mounted.

If you don't want to see their icons on the desktop, just open Menu -> Settings Manager -> Desktop -> Icons (tab) and uncheck "Removable Devices".