Javascript to compute max width and height for a nested HTML element
What is

parseInt((control.outerHeight(true)) - control.height());


supposed to achieve?

The result of - is always going to be a number, so what this does is convert the number to a string and back to a number.  This can only lose precision and waste time.

Similarly, the use of parseInt on the first argument is also unnecessary

parseInt(control.parent().height()) - heightBuffer(control)


since

"4" - 1 === 3


In fact, the automatic conversion that - does is better than that done by parseInt since parseInt falls back to octal on some interpreters but not others.

"10"             - 1 === 9
parseInt("10")   - 1 === 9
"0x10"           - 1 === 15
parseInt("0x10") - 1 === 15
"010"            - 1        // throws reliably
parseInt("010")  - 1 === 7  // on some and 9 on others


so I'd get rid of all the uses of parseInt as an operand to -.

You seem to be setting min-height but the method is called MaxHeight.  That confuses me.

When you change the CSS

control.css('min-height', h)


you might want to specify units as in

control.css('min-height', h + "px")


I'm not sure how you're handling the widths of margins and borders on the controls.  Is that important to you?