How do I determine where on the screen the child form will appear? Is it a property
>of the child form?

You can actually tell the child form where you want it to appear when you call it like so:

Code in Parent form to instatiate child form:

LOCAL luValue, lnTop, lnLeft

*** Calculate where the popup form should be instantiated
*** So it pops up directly below this control
*** SYSMETRIC( 9 ) is the height of the Form's title bar in case you were curious

lnTop = OBJTOCLIENT( Thisform, 1 ) + OBJTOCLIENT( This, 1 ) + This.Height + ;
              IIF( Thisform.TitleBar = 1, SYSMETRIC( 9 ) + 2, 2 )
lnLeft = OBJTOCLIENT( Thisform, 2 ) + OBJTOCLIENT( This, 2 )
DO FORM MyForm WITH lnTop, lnLeft TO luValue

Code in the init of the child form:

LPARAMETERS tnTop, tnLeft
WITH Thisform
  *** Position it correctly
  .Top = tnTop
  .Left = tnLeft
ENDWITH