  The Borromean nucleus $^{17}$Ne ($^{15}$O$ + p + p$) is investigated by using
the hyperspheric adiabatic expansion for a a three-body system. The measured
size of $^{15}$O and the low-lying resonances of $^{16}$F ($^{15}$O$ + p$) are
first used as constraints to determine both central and spin-dependent two-body
interactions. Then, the ground state structure of $^{17}$Ne is found to be an
almost equal mixture of $s^2$ and $d^2$ proton-$^{15}$O relative states, the
two lowest excited states have about 80% of $sd$-mixed components, and for the
next two excited three-body states the proton-$^{15}$O relative s-states do not
contribute. The spatial extension is as in ordinary nuclei. The widths of the
resonances are estimated by the WKB transmission through the adiabatic
potentials and found in agreement with the established experimental limits. We
compare with experimental information and previous works.
