The effects of a strong quantizing magnetic field on the nucleation of quar
k matter droplets and on the chemical evolution of a nascent quark phase at
the core of a magnetar are investigated. The surface energy of the quark p
hase diverges logarithmically. As a consequence there cannot be a first ord
er transition to the quark phase. However, a metal-insulator type of second
order transition is possible unless the field strength exceeds 10(20) G. T
he study of the chemical evolution of a newborn quark phase shows that in b
eta equilibrium the system becomes energetically unstable.