  The zero temperature phase diagram of the mono-axial chiral helimagnet in the
magnetic field plane formed by the components parallel and perpendicular to the
helical axis is thoroughly analyzed. The nature of the transition to the
commensurate state depends on the angle between the field and the helical axis.
For field directions close to the directions parallel or perpendicular to the
helical axis the transition is continuous, while for intermediate angles the
transition is discontinuous and the incommensurate and commensurate states
coexist on the transition line. The continuous and discontinuous transition
lines are separated by two tricritical points with specific singular behaviour.
The location of the continuous and discontinuous lines and of the tricritical
points depend strongly on the easy-plane anisotropy, the effect of which is
analyzed. For large anisotropy the conical approximation locates the transition
line very accurately, although it does not predict the continuous transitions
nor the tricitical behaviour. It is shown that for large anisotropy, as in
CrNb3S6, the form of the transition line is universal, that is, independent of
the sample, and obeys a simple equation. The position of the tricritical
points, which is not universal, is theoretically estimated for a sample of
CrNb3S6
