As we move away from the centre of, say, a spiral galaxy, is there a relation between the stellar mass and distance? I know the how the stellar abundance and density varies with the distance but does stellar mass also follow a pattern?
In terms of the distribution of stellar masses when stars form -- the Initial Mass Function (IMF) -- there doesn't seem to be much variation, at least for spirals. (There is evidence that massive elliptical galaxies may have different IMFs as a function of radius, with relatively more low-mass stars formed near their centers. The cause of this is unclear; it might have to do with different conditions for star formation, with very dense, high-pressure gas in what would become the centers of massive elliptical galaxies possibly producing different distributions of stellar masses.)
The current distribution of stellar masses at a given radius in a spiral galaxy will depend almost entirely on the local star-formation history. Since stellar lifetime depends on stellar mass, regions with recent star formation will have more stars that are massive; regions where star formation ceased a long time ago will be dominated by low-mass stars, since all the higher-mass stars there have died.
In most spiral galaxies, the mean age of stars tends to decrease as you move further out in radius (as indicated by optical colors: reddish central regions are mostly old populations dominated by red giants, while the disk further out is blue because there are younger populations dominated by hot, massive stars). This is an example of what's called "inside-out" star formation.
However, a lot of lower-mass spirals seem to show a reversal of this trend at large radii, with redder (older, mostly lower-mass) stars beyond a certain radius. Since this is the same radius at which the density of stars in the disk stars falling off more rapidly (the "break" or "truncation" radius), it's usually thought this is the result of a combination of two effects: 1) A radial threshold/cutoff in star formation, with very few stars being formed beyond a certain radius (possibly because the gas density becomes too low); and 2) Radial scattering of stars over time by spiral arms, which means that older stars tend to be scattered to larger (or smaller) radii simply because they've had more encounters with spiral arms. In this case, the relative fraction of more massive stars would increase with radius out to the truncation radius, and then decrease beyond.