I use the following AutoHotKey script to activate LogMeTT and set the View Connection Tree to maximize. This is a snippit of my always running AutoHotkey startup script. I use the "Windows Y" key combination to activate LogMeTT. You can modify to use any hotkey combination of your choice.
coordmode, mouse, screen
If you are not familiar with AutoHotkey, their site is: http://www.autohotkey.com
; Tie this routine to the "Windows Y" key combination
; Change the coordinate mode to screen so that absolute screen position can be used. This assumes the LogMeTT tray icon is always in the same position.
; Double left click on absolution screen position x=1464, y=885. This is the position of my LogMeTT icon in the tray. You can find yours by using the AutoHotKey "Window Spy" utility
; Wait 2 seconds (2000 mseconds) for LogMeTT window to appear
; Send these keys - Alt-V, Down Arrow, Right Arrow, Down Arrow - to maximize the Connection Tree
; Done with this routine so return