  We report a study of the ferromagnetism of ZrZn$_{2}$, the most promising
material to exhibit ferromagnetic quantum criticality, at low temperatures $T$
as function of pressure $p$. We find that the ordered ferromagnetic moment
disappears discontinuously at $p_c$=16.5 kbar. Thus a tricritical point
separates a line of first order ferromagnetic transitions from second order
(continuous) transitions at higher temperature. We also identify two lines of
transitions of the magnetisation isotherms up to 12 T in the $p-T$ plane where
the derivative of the magnetization changes rapidly. These quantum phase
transitions (QPT) establish a high sensitivity to local minima in the free
energy in ZrZn$_{2}$, thus strongly suggesting that QPT in itinerant
ferromagnets are always first order.
