  Phase transformation in finite-size ferroelectrics is of fundamental
relevance for understanding collective behaviors and balance of competing
interactions in low-dimensional systems. We report a first-principles effective
Hamiltonian study of vortex-to-polarization transformation in
Pb(Zr$_{0.5}$Ti$_{0.5}$)O$_3$ nanoparticles, caused by homogeneous electric
fields normal to the vortex plane. The transformation is shown to (1) follow an
unusual {\it macroscopic} path that is symmetry non-conforming and
characterized by the occurrence of a previously unknown structure as the
bridging phase; (2) lead to the discovery of a striking collective phenomenon,
revealing how ferroelectric vortex is annihilated {\it microscopically}.
Interactions underlying these behaviors are discussed.
