Percentage of Neutron Stars that leave the Galaxy When a neutron star(NS) is born the supernova kick gives the newborn NS a certain boost in a supposed isotropic direction and, depending on how strong the boost is and on the position of the NS at birth time, its kinetic energy might exceed its gravitational potential one and the NS will definitely leave the galaxy.
For what I found in literature the absolute value of the kick velocity follows a Maxwellian distribution with a mode value around 400 km/s.
With this in hand, together with a certain model for the galactic potential and initial spatial distribution, isn't it trivial to find the percentage of NS that eventually leave the galaxy?
I ask this because I cannot find anything about it in literature.
 A: A recent study by Verbunt et al. (2017) models the pulsar speed distribution as the sum of two Maxwellians, one with a sigma of $\sim 80$ km/s and the other with a sigma of $\sim 330$ km/s. About 30% of the population are in the low speed Maxwellian. A plot of the (model) distribution is shown in Fig.9 of that paper.
The figures quoted above are for young pulsars. This is important for your question because older neutron stars might form a biased population where they have undergone significant acceleration and/or the most rapid ones have already escaped (and indeed the model distribution for all pulsars shows fewer fast-moving objects as a fraction of the whole).
To answer your question though is non-trivial and probably requires an accurate model of the Galactic potential. A starting point would be to assume that the observed population originates in the Galactic plane (since they originate from young, massive stars) and that the observed velocity distribution represents the natal distribution. The Galactic escape speed is probably a function of Galactocentric radius. Piffl et al. (2018) estimate a local escape speed of $537^{+59}_{-43}$ km/s, increasing to $>600$ km/s at Galactocentric radii $<4 $kpc and decreasing to about 500 km/s at Galactocentric radii $>11$ kpc. This variation is perhaps small enough that we could take a value of 550 km/s as typical for the necessary escape speed in the pulsar sample. In which case, I would estimate the fraction of young pulsars that will escape to be $\sim 25$%, though you could presumably use Verbunt's model parameters to get a more precise (though not necessarily more accurate) result.
A: I couldn't tell you exactly what percentage of neutron stars leave the galaxy, neither could anybody else, but it must be a very tiny percentage indeed. After a supernova explosion, most neutron stars stay  where they are. If you look at supernova remnants, there is usually a neutron star at the dead centre. To send the neutron star flying off like an outsize cannonball, the supernova would have to be asymmetrical, but  very few are. It does sometimes happen, but I would think the supernova would have to be on the outskirts of the galaxy for the neutron star to leave the galaxy altogether.
