  We present a tidal model for treating the rotational evolution in the general
three-body problem with arbitrary viscosities, in which all the masses are
considered to be extended and all the tidal interactions between pairs are
taken into account. Based on the creep tide theory, we present the set of
differential equations that describes the rotational evolution of each body, in
a formalism that is easily extensible to the N tidally-interacting body
problem. We apply our model to the case of a circumbinary planet and use a
Kepler-38 like binary system as a working example. We find that, in this low
planetary eccentricity case, the most likely final stationary rotation state is
the 1:1 spin-orbit resonance, considering an arbitrary planetary viscosity
inside the estimated range for the solar system planets. We derive analytical
expressions for the mean rotational stationary state, based on high-order power
series of the semimajor axes ratio a1 /a2 and low-order expansions of the
eccentricities. These are found to reproduce very accurately the mean behaviour
of the low-eccentric numerical integrations for arbitrary planetary relaxation
factors, and up to a1/a2 \sim 0.4. Our analytical model is used to predict the
stationary rotation of the Kepler circumbinary planets and find that most of
them are probably rotating in a sub-synchronous state, although the synchrony
shift is much less important than the one estimated in Zoppetti et al. (2019,
2020). We present a comparison of our results with those obtained with the
Constant Time Lag and find that, unlike what we assumed in our previous works,
the cross torques have a non-negligible net secular contribution, and must be
taken into account when computing the tides over each body in an
N-extended-body system from an arbitrary reference frame. These torques are
naturally taken into account in the creep theory.
