|A proven procedure is using the IE shortcut icon, right click and select Properties.|
In it's Run box change it to Maximized. Click Apply and Ok.
Using that shortcut launch IE.
Using any link on that page, right click and select Open in a New Window.
Click and drag the title bar to the top left of the screen.
Wave the cursor over the lower right hand corner to get the cursor to change to the double sided arrow. Then click and drag it to the lower right hand corner of the viewable screen. (simulating the maximum size of the window)
Now close (exit) the original window and then exit the new window. (in that order)
From then on all windows will open as such.
Note: There is no such thing as a New Window opening "Maximized".