When will s/he walk unsupported? depending on temperament, body build, gender, and family environment, babies vary from taking just a few days to several weeks as they transform into true bipeds. For instance, more cautious children may rely on this supported cruising for weeks or even months: occasionally a sudden fall or unexpected change in daily routine my even cause them to revert to crawling again as they reconsider their moves. (Don't worry: the sequence from standing to cruising to walking take less time on his/her second go-round.) "Overall, we'd want to refer a baby for evaluation if s/he isn't walking by 16 months, to assess his/her motor skills.
No matter when your baby takes those first steps toward independence, it will probably be because s/he has forgotten that they were doing something risky. "They'll step away from whatever they were holding on to because of what motivated them (ie. toys) Then s/he will likely be so astonished by their own victory that they'll want to try it again.