Homogeneous hydrogenations of unsaturated substrates with parahydrogen yield strong NMR signal enhancements of the transferred H-1 nuclei if the symmetry of H-2 is broken in the resulting hydrogenated products. This chemically induced hyperpolarization known as Parahydrogen-induced polarization (PHIP) is also transferred to other protons and heteronuclei (H-2, C-13, Si-29, P-31) when the hydrogenation is initiated at low magnetic fields. Hydrogenating various fluorinated styrenes and phenylacetylenes, we show that PHIP-derived hyperpolarization is transferred to F-19 not only in the Earth's magnetic field (ALTADENA condition) but also in a strong magnetic field, e.g., when carrying out the reaction in the NMR spectrometer (PASADENA condition). Upon conducting a systematic analysis of the observed PHIP transfer to H-1, C-13, and F-19 in the hydrogenation products to elucidate the mechanisms that govern this parahydrogen-aided resonance transfer (PART), we conclude that high-and low-field PHIP transfer mechanisms differ in detail depending on either through-bond or through-space interactions. Substrates with high hydrogenation rates and long spin-lattice relaxation times (T-1) yield the highest degree of heteronuclear hyperpolarization. Possible medical applications for hyperpolarized F-19-containing molecules as "active" contrast agents for magnetic resonance imaging (MRI) are outlined.