If you use a custom layout, you can save the size and position of floating views such as the Render Tree.
In the online User’s Guide, look up windows:setting default size and position.

You could also use a toolbar button to run a script that opens the render tree with the desired size and position. For example:

var layout = Application.Desktop.ActiveLayout;
var v = layout.CreateView( "Render Tree", "Render Tree" );
v.Move( 10, 10 );
v.Resize( 1000,1000 );