Random constructions and density results

In this paper we outline a construction method which has been used for minimal blocking sets in PG(2, q) and maximal partial line spreads in PG(n, q) and which must have a lot of more applications. We also give a survey on what is known about the spectrum of sizes of maximal partial line spreads in PG(n, q). At the end we list some more elaborate random techniques used in finite geometry.