  We compute the muon to electron conversion in the type-I seesaw model, as a
function of the right-handed neutrino mixings and masses. The results are
compared with previous computations in the literature. We determine the
definite predictions resulting for the ratios between the muon to electron
conversion rate for a given nucleus and the rate of two other processes which
also involve a mu-e flavour transition: mu -> e gamma and mu -> eee. For a
quasi-degenerate mass spectrum of right-handed neutrino masses -which is the
most natural scenario leading to observable rates- those ratios depend only on
the seesaw mass scale, offering a quite interesting testing ground. In the case
of sterile neutrinos heavier than the electroweak scale, these ratios vanish
typically for a mass scale of order a few TeV. Furthermore, the analysis
performed here is also valid down to very light masses. It turns out that
planned mu -> e conversion experiments would be sensitive to masses as low as 2
MeV. Taking into account other experimental constraints, we show that future mu
-> e conversion experiments will be fully relevant to detect or constrain
sterile neutrino scenarios in the 2 GeV-1000 TeV mass range.
