We have performed magnetic and transport measurements on La0.7Ca0.3MnO3 polycrystalline pellets and thin films. We propose a model that reproduces very well the low-field and high-field magnetoresistance at low temperature. The decrease of the resistance at high fields is modeled by the opening of new conduction channels in parallel due to the ordering of Mn spins blocked at the grain surface. We found that high-field magnetoresistance is independent of grain size, at least down to 12 nm, but depends strongly on the connectivity between grains. (C) 1999 American Institute of Physics. [S0003-6951(99)04524-6].