Sure. No big deal, heres the simple and but not so perfect method.
There's no way to maximize but make it that big is possible. First lets make the window in a proper manner:
string $window = `window -title "my secondary window" gSecondaryWindow`;
paneLayout;
modelPanel;
showWindow $window;
Now maya will record the size and position of this window, if you change it maya will remember next time you build the window with the same name. (beware maya will NOT remember maximization, and some older Mayas bug so after sizing move the toolbar a bit if it refuses to cooperate).
Now then you need to recreate this window every file open (in case it will break, in older mayas it does). to do this lets change the previous a bit:
global proc jooBuildMySecondaryWindow(){
if (`window -ex gSecondaryWindow`)
deleteUI gSecondaryWindow;
string $window = `window -title "my secondary window" gSecondaryWindow`;
paneLayout;
modelPanel;
showWindow $window;
}
and put it in a file named jooBuildMySecondaryWindow.mel or whatever you choose to name the proc (its important the name MUST match). Place this file in your scripts folder usually documents\maya\scripts\ but YMMV. you don't really need the if clause in all maya versions but ok it there to keep you out of trouble if you do.
then locate your userSetup.mel if it does not exist create one, to find if you have you try whatIs userSetup inside maya to locate it.
put this line in userSetup.mel:
scriptJob -event SceneOpened jooBuildMySecondaryWindow;
restart maya and you should be good to go.
You can put more stuff in the window. Better yet you can make it a scripted panel then maya will remember its state between saves. And you then don't need to launch it as much, this is handy if you for example decide to split the panel in two with graph editor on the bottom. now maya will load the window in that state, etc etc. You can also eliminate the nee dto reload it all the time. But this should get you going.
PS: lack of programmatic maximization kid of sucks, thsi could be easily fixed with pyqt or by making a command that calls the oses functions but yeah i wont bother i never actually maximize anything personally. Whats the point, if you allays maximize all your software then what use is it to have a windowing system?