The interpretation of the role of dark matter in the Universe depends on the model of dark matter under consideration. Some models assume for example that dark matter is confined inside compact stars. In this case you can consider the presence of dark matter everywhere.

some standard model which explained the signature of dark matter indirectly . " indirectly means we can observe the effect of its presence . that effect were seen in the halos of milky ways , its stars motion , lensing ...infact through this model , presence of local dark matter were explained too. (in our solar system) . its distribution might not so good and its density would be very small per cc . may be still due to the lack of highly technological civilisation its sign cant be shown everywhere.

i think its presence is not only outside the galaxy , might be anywhere in the universe ..

It is densest within the galaxy and becomes thinner outside. The approximations to the profile can be seen in these articles:

https://en.wikipedia.org/wiki/Navarro%E2%80%93Frenk%E2%80%93White_profile

https://en.wikipedia.org/wiki/Einasto_profile

The profile is related to the Virial Theorem.

The dark matter inferred from rotation curves of spiral galaxies (assuming Newtonian gravitation) is seen from observations to be dominant in the external parts because the ratio of the local gravitational mass (deduced from the rotation curve) to the mass detected by other means (stars, gas, dust) increases with the distance to the galaxy centre. Since the nature of dark matter is still unknown (otherwise it would not be called dark matter), every dark matter candidate (such as WIMPs, MACHOs, cold gas, black holes) or alternative gravitation theories should provide and explanation why the dark/observed matter ratio increases with radius.

A related fact that is rarely discussed is that the dark/neutral-atomic-hydrogen ratio is rather constant in individual spirals (Bosma 1981), which was a motivation for us to investigate the possibility to hide baryons with very cold molecular hydrogen (Pfenniger Combes 1994). The detected atomic gas (H) would be only the visible phase of hydrogen most of the time in the form of dense molecular gas (H2) at very low temperature (3-7K).

In the mean time the amount of detected cold gas has doubled (the so-called "dark gas") but is still insufficient to fully explain the rotation curves. Another hint that undetected molecular gas exists in the outer atomic gas disk is that meanwhile a very faint population of forming stars has been detected in the UV. Since stars form from molecular gas, not atomic gas, some additional undetected molecular gas must exist in the observed atomic gas disks.