On a magnetar, which force would exert a bigger pull on a 10 kg iron chunk? On the surface of a magnetar, what would pull harder on a 10 kg piece of iron, the gravity or the magnetic field?
 A: Ferromagnitism
Below saturation, the pull is ~B dB/dx. Beyond saturation, it is ~dB/dx and can be made arbitrarily high with a strong enough gradient. An order of magnitude gradient is 1GT/10km = 10^5T/m. So a pull on the order of 10^5-10^6 stronger than a Neodymium magnet. We have about 2*10^11g of gravity so gravity wins.
Superconductors and Paramagnetism
They also suffer a saturation effect. Superconductors can only carry a certain density of current and paramagnetic materials saturate much like ferromagnetic materials. Paramagnetism aligns dipoles and saturates once there are no more dipoles to align.
Diamagnetism
This is much weaker but also doesn't saturate. It is about 10^4 times weaker at best and thus would equal ferromagnetism around 10^4 or 10^5 T. At 10^10 T it would be around (10^10T*10^5T/m)/(10^4) = 10^11 times stronger than a Neodymium magnet. This is just enough to beat gravity. However, "doesn't saturate" is not true at such extreme fields, see below.
Edit: Argument that diamagnetism is limited: Diamagnetism costs energy. Free electrons and nuclei are not diamagnetic. If this energy cost exceeded the binding energy of all the electrons to the iron nucleus the atom would fly apart. This limits the total diamagnetic energy to below ~100keV/atom. I do not expect the atoms to actually ionize in the field, instead the electrons would find a non-diamagnetic configuration, but the 100keV limit still applies. Gravity is far stronger at ~10GeV per iron atom.
Materials, what materials?
Magnetic fields this strong severely distort the shape of the atoms due to Lorentz force affecting the electron shells. Laboratory-generated fields top out around 1000 Tesla and only for under a millisecond. Whatever the case gravity still wins. After all, the crust doesn't lift off the surface!
A: Iron is nothing special to a magnetar: iron's magnetization saturates at about 2 tesla. Magnetar fields are 10^9-10^11 tesla. So, gravity wins.
