  We analyse by numerical simulations and scaling arguments the avalanche
statistics of 1-dimensional elastic interfaces in random media driven at a
single point. Both global and local avalanche sizes are power-law distributed,
with universal exponents given by the depinning roughness exponent $\zeta$ and
the interface dimension $d$, and distinct from their values in the uniformly
driven case. A crossover appears between uniformly driven behaviour for small
avalanches, and point driven behaviour for large avalanches. The scale of the
crossover is controlled by the ratio between the stiffness of the pulling
spring and the elasticity of the interface; it is visible both in the global
and local avalanche-size distributions, as in the average spatial avalanche
shape. Our results are relevant to model experiments involving locally driven
elastic manifolds at low temperatures, such as magnetic domain walls or vortex
lines in superconductors.
