  We consider isogeometric discretizations of the Poisson model problem,
focusing on high polynomial degrees and strong hierarchical refinements. We
derive a posteriori error estimates by equilibrated fluxes, i.e., vector-valued
mapped piecewise polynomials lying in the $\boldsymbol{H}({\rm div})$ space
which appropriately approximate the desired divergence constraint. Our
estimates are constant-free in the leading term, locally efficient, and robust
with respect to the polynomial degree. They are also robust with respect to the
number of hanging nodes arising in adaptive mesh refinement employing
hierarchical B-splines. Two partitions of unity are designed, one with larger
supports corresponding to the mapped splines, and one with small supports
corresponding to mapped piecewise multilinear finite element hat basis
functions. The equilibration is only performed on the small supports, avoiding
the higher computational price of equilibration on the large supports or even
the solution of a global system. Thus, the derived estimates are also as
inexpensive as possible. An abstract framework for such a setting is developed,
whose application to a specific situation only requests a verification of a few
clearly identified assumptions. Numerical experiments illustrate the
theoretical developments.
