  We use the Gemini NIFS instrument to map the H$_2 2.1218\mu$m and Br$\gamma$
flux distributions in the inner 0.04-2 kpc of a sample of 36 nearby active
galaxies ($0.001\lesssim z\lesssim0.056$) at spatial resolutions from 4 to 250
pc. We find extended emission in 34 galaxies. In $\sim$55% of them, the
emission in both lines is most extended along the galaxy major axis, while in
the other 45% the extent follows a distinct orientation. The emission of H$_2$
is less concentrated than that of Br$\gamma$, presenting a radius that contains
half of the flux 60% greater, on average. The H$_2$ emission is driven by
thermal processes - X-ray heating and shocks - at most locations for all
galaxies, where $0.4<H_2/Br\gamma<6$. For regions where H$_2$/Br$\gamma>6$
(seen in 40% of the galaxies), shocks are the main H$_2$ excitation mechanism,
while in regions with H$_2$/Br$\gamma<0.4$ (25% of the sample) the H$_2$
emission is produced by fluorescence. The only difference we found between type
1 and type 2 AGN was in the nuclear emission-line equivalent widths, that are
smaller in type 1 than in type 2 due to a larger contribution to the continuum
from the hot dusty torus in the former. The gas masses in the inner 125 pc
radius are in the range $10^1-10^4$ M$_\odot$ for the hot H$_2$ and $10^3-10^6$
M$_\odot$ for the ionised gas and would be enough to power the AGN in our
sample for $10^5-10^8$ yr at their current accretion rates.
