We present spatially resolved Hubble Space Telescope grism spectroscopy of 15 galaxies at $zsim0.8$ drawn from the DEEP2 survey. We analyze H$alpha$+[N II], [S II] and [S III] emission on kpc scales to explore which mechanisms are powering emission lines at high redshifts, testing which processes may be responsible for the well-known offset of high redshift galaxies from the $zsim0$ locus in the [O III]/H$beta$ versus [N II]/H$alpha$ BPT (Baldwin-Phillips-Terlevich) excitation diagram. We study spatially resolved emission line maps to examine evidence for active galactic nuclei (AGN), shocks, diffuse ionized gas (DIG), or escaping ionizing radiation, all of which may contribute to the BPT offsets observed in our sample. We do not find significant evidence of AGN in our sample and quantify that, on average, AGN would need to contribute $sim$25% of the H$alpha$ flux in the central resolution element in order to cause the observed BPT offsets. We find weak ($2sigma$) evidence of DIG emission at low surface brightnesses, yielding an implied total DIG emission fraction of $sim$20%, which is not significant enough to be the dominant emission line driver in our sample. In general we find that the observed emission is dominated by star forming H II regions. We discuss trends with demographic properties and the possible role of $alpha$-enhanced abundance patterns in the emission spectra of high redshift galaxies. Our results indicate that photo-ionization modeling with stellar population synthesis inputs is a valid tool to explore the specific star formation properties which may cause BPT offsets, to be explored in future work.
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