  We consider the possible existence of self-similar solutions containing black
holes in a Friedmann background with a stiff fluid or a scalar field. We
carefully study the relationship between the self-similar equations in these
two cases and emphasize the crucial role of the similarity horizon. We show
that there is no self-similar black hole solution surrounded by an exact or
asymptotically flat Friedmann background containing a massless scalar field.
This result also applies for a scalar field with a potential, providing the
universe is decelerating. However, if there is a potential and the universe is
accelerating (as in the quintessence scenario), the result only applies for an
exact Friedmann background. This extends the result previously found in the
stiff fluid case and strongly suggests that accretion onto primordial black
holes is ineffective even during scalar field domination. It also contradicts
recent claims that such black holes can grow appreciably by accreting
quintessence. Appreciable growth might be possible with very special matter
fields but this requires {\it ad hoc} and probably unphysical conditions.
