  We perform a search for faint, common proper motion companions of Hipparcos
stars using the recently published LSPM-north catalog of stars with proper
motion mu>0.15 arcsec/yr. Our survey uncovers a total of 521 systems with
angular separations 3 arcsec < Delta theta < 1500 arcsec, with 15 triples and 1
quadruple. Our new list of wide systems with Hipparcos primaries includes 130
systems identified here for the first time, including 44 in which the secondary
star has V>15.0. Our census is statistically complete for secondaries with
angular separations 20 arcsec < Delta theta < 300 arcsec and apparent
magnitudes V<19.0. Overall, we find that at least 9.5 % of nearby (d<100 pc)
Hipparcos stars have distant stellar companions with projected orbital
separations s > 1,000 AU. We observe that the distribution in orbital
separations is consistent with Opik's law f(s) ds ~ s^{-1} ds only up to
separation s \approx 3,000 AU, beyond which it follows a more steeply
decreasing power law f(s) ds ~ s^{-l} ds with l=1.6+/-0.1. We also find that
the luminosity function of the secondaries is significantly different from that
of the single stars field population, showing a relative deficiency in
low-luminosity (8<M_V<14) objects. The observed trends suggest either a
formation mechanism biased against low-mass companions, or a disruption over
time of systems with low gravitational binding energy.
