  We study the phenomenology of recoil-free jet axes using analytic
calculations and Monte Carlo simulations. Our focus is on the average energy as
function of the angle with the jet axis (the jet shape), and the energy and
transverse momenta of hadrons in a jet (TMD fragmentation). We find that the
dependence on the angle (or transverse momentum) is governed by a power law, in
contrast to the double-logarithmic dependence for the standard jet axis. The
effects of the jet radius, jet algorithm, angular resolution and grooming are
investigated. TMD fragmentation is important for constraining the structure of
the proton through semi-inclusive deep-inelastic scattering. These observables
are also of interest to the LHC, for example to constrain $\alpha_s$ from
precision jet measurements, or probe the quark-gluon plasma in heavy-ion
collisions.
