Hi Dave, I'm using the script from the "Self-Paced Reading Task" (noncumulative) from the task library. These are the only changes that I made to that script: 
1) replaced "-" with "" in:
<values userparams>
[....]
/ ucmaskchar = ""
/ lcmaskchar = ""
</values>
2) as you suggested, the text.mywindow is now centered: 
<text mywindow>
[.....]
/ vjustify = center
/ hjustify = center
[.....]
</text>
3) (optional) to easily test whether the windows are centered, I'm using the following item. The "C" indicates the center of the window; so the "C" of the different windows should appear in the same position on the screen (center). 
/ 1 ="|1xxxxCxxx x|2xxC xx|3xx xCxxxxx|4xxxxxxxxC xxxxxxxx|5xxCxxx|"
As mentioned in my previous message, all windows are centered except the first, which is a bit on the left. Below is an example: windows 2-5 have the center ("C" in my example) in the same position on the screen, but window1 is a bit on the left, that is, its center is on the left of the center of all other windows. In this illustration pretend that "|" is the boundary of the screen: 
window1: |      1xxxxCxxx x          |
window2: |          2xxC xx          |
window3: |        3xx xCxxxxx        |
window4: |    4xxxxxxxxC xxxxxxxx    |
window5: |          5xxCxxx          |See also the picture attached (screenshots of the first three windows). As you can see from the red line that I added, windows 2-3 (and the following windows) are aligned in the center; the first window is a bit on the left. 

I hope, I explained it more clearly. 
Please let me know if you would like me to attach the task too. 
Thank you, 
Luca