It is claimed Albanians demographically grew there in the early Ottoman period through constant mass immigration, these Albanians apparently also were encouraged by the Ottomans to settle and were given special rights. Let's see what the evidence says:

15th and 16th century:

Serbian historians explain the growth of an Albanian population in Kosovo during the early Ottoman period in terms of physical immigration: it is suggested that Albanians from the Malesi were encouraged by the Ottomans to settle in Kosovo, that many of these turned to Islam to gain the advantages of superior status, and that those Slavs who became Muslims were not merely Islamicized but, sooner or later, Albanianized as well. Although the Albanian historians' argument seems unconvincing for general reasons, it nevertheless comes buttressed with some intriguing evidence from the Ottoman registers. The Ottoman officials usually noted which heads of family were 'new arrivals’ in their places of residence; out of 121 new arrivals in the nahiye of Pec in 1485, the majority had Slav names. In the sancak of Prizren in 1591, only five new arrivals out of forty-one bore Albanian names; and in a group of Kosovo towns in the 1580s and 1590s there were twenty-five new Albanian immigrants and 133 with Slav names - several of them described as coming from Bosnia. This evidence counts strongly against the idea of a mass immigration from northern Albania. Other more general arguments against that idea are based on relative population sizes and rates of growth. The population of Kosovo during this period was much bigger than that of northern and central Albania, and its rate of growth was actually lower. This is not what one would expect if a large overflow from the Albanian Malesi were flooding into Kosovo.
17th Century:

Some of the Catholic documents also note cases of Albanians moving into Kosovo from northern Albania. Pjeter Mazrreku reported from Prishtina in 1624: 'not long ago ten Catholic families came from Albania to live in this area’; in Suha Reka in 1637 Gjergj Bardhi found fifteen Catholic families who had fled there from the Dukagjin mountains because of 'assassins'; and Gregor Mazrreku found several Albanians at a nearby village in 1651, who had also ‘fled from the mountains’. Gregor Mazrreku noted that most of these had become Muslims since their arrival. It seems likely that people fled from the Malesi either because of blood-feuds or because they had been punished under the Kanun of Lek Dukagjin (which, it will be recalled, said that people guilty of serious crimes should have their houses burnt down and be expelled). Such people, arriving ina new area, would naturally feel more unattached to the local Catholic community, and would be more easily tempted to make the switch to Islam. Larger groups emigrating together were much more rare; but in these cases there was more religious cohesion. A group of thirty-five Catholic Albanian families from Albania was noted at the mining town of Kratovo, east of Skopje, in 1637; they were already learning the Slav language, and it is likely that they were eventually assimilated by the local Slav-speaking Catholic community. Overall, however, one conclusion is certain: the number of people migrating into the Kosovo area from northern Albania during this period was, relative to the already existing Albanian population of Kosovo, extremely small. The Malesi was almost entirely Catholic; the reports by the Catholic priests in Kosovo are thorough and very detailed; and it is not possible to imagine that many thousands of Catholic immigrants could have escaped their notice - even (or, perhaps, especially) if they did not remain Catholic for long.
- Kosovo: A Short History