We thank the referee for their constructive additional suggestions.
All corresponding changes have been marked in blue.

> For the Figure 2 y-axis label, perhaps just put “Field Strength”. As it is
> very uncommon to leave an axis unlabelled.

We have now added "Field Strength" on the y axis; see page 4.

> Page 8 “the kinetic energy loss is particularly strong around the Alfen
> surface; see Figure 7.” – Alfven typo error.

We have now corrected this; see left column of page 8.

> In Figure 10 the authors say the quantities plotted are an averaged Jdot,
> how exactly is this done? Do you follow the field line at theta=70deg and
> integrate the domain above and below? Or do you integrate the values in a
> cone above and below theta=70deg? I think the first method is the most
> applicable, because the use of a cone will truncate some of the flow as it
> diverges towards the equator and vice versa. Is this the cause of the sharp
> v-like structures in Figure 10? Often the AM flux along a magnetic field
> line is compared, rather than averaged values. See a recent example from
> Pantolmos & Matt 2017, where they compare the flow speed along different
> magnetic field lines (their Figure 3 and 4). Though in the authors’ case, I
> would indeed perform an average over the flow emanating above and below 70
> degrees (but being careful to appropriately follow the boundary of these
> flows).

Yes, it is done over cones; we have now used the word "cone" this in the
text; see bottom of page 9. The v-shaped profiles of the angular momentum
flux are just a consequence of a sign change when plotting the logarithm
of the *modulus* of the angular momentum flux. We have now mentioned the
potential advantage of studying the AM flux along field lines. However,
because of the unsteady character of the solution, the advantage is no
longer that obvious.

> Figure 11 is very informative. This, in addition to the extra discussion of
> the negative tangential wind speeds, makes the results of this work far
> easier to digest. I am still intrigued about the cause of the negative
> tangential wind speeds. Is this a result of non-radial flow at the stellar
> surface? If so, perhaps the lack of a “realistic” photosphere, or
> sufficient boundary conditions at this layer, is linked? It might be
> fitting to mention this in Section 3.8. I would be interested to hear the
> authors’ opinions on this, even if no text is added to the manuscript.

We have now added a new paragraph at the end of Sect.3.8 where we show that,
as a consequence of unrealistically low densities in the stellar envelope,
the surface rotational velocity can be retrograde at certain times and at
some latitudes. This is now shown in the new Fig.18.

> Is it possible in Figure 16 to also show the solar case, as you reference
> Figure 10 in the text for comparison however this figure does not average
> over all latitudes (this would also reassure the reader that the global
> angular momentum-loss rate for the solar case is positive, despite the
> negative contributions at midlatitudes). Additionally, it would be
> informative to also plot the total angular momentum flux in Figure 16,
> which will show how steady the global angular momentum-loss rate is for a
> given snapshot in time.

We have now added panel (a) for Model A. We emphasize that in Model~A,
the net angular momentum transport is negative when averaged over
all latitudes. This is now said more clearly on page 10 (left column)
where we say that the negative AM flux dominates. The total (kinetic,
magnetic, and viscous) angular momentum transport is dominated by the
kinetic contribution, except for Model A, where the magnetic contribution
is rather strong when considering the time average, but negative in the
outer parts. We have now mentioned this in the caption to Figure 16.