\header {
  tagline = ##f
}

#(define (printable-height layout props)
   (let
    ((height (ly:output-def-lookup layout 'paper-height))
     (tm (ly:output-def-lookup layout 'top-margin))
     (bm (ly:output-def-lookup layout 'bottom-margin)))
    (- height tm bm)))

#(define-markup-command (vertical-fill layout props height mups) (number? markup-list?)
   (let*
    ((realheight (if (>= height 0) height (printable-height layout props)))
     (tmu (stack-lines -1 0.0 0 (interpret-markup-list layout props mups)))
     (muext (ly:stencil-extent tmu Y))
     (muheight (- (cdr muext) (car muext)))
     (noels (length mups))
     (space (if (> noels 1) (/ (- realheight muheight) (- noels 1)) 0))
     (mu (if (> noels 1)
             (stack-lines -1 0.0 space (interpret-markup-list layout props mups))
             (if (= noels 0) empty-stencil
               (interpret-markup layout props (car mups))))))
    mu))

\markup \vertical-fill #-1 { a b \column { c d e } }