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We perform a search for faint, common proper motion companions of Hipparcosstars using the recently published LSPM-north catalog of stars with propermotion mu>0.15 arcsec/yr. Our survey uncovers a total of 521 systems withangular separations 3 arcsec < Delta theta < 1500 arcsec, with 15 triples and 1quadruple. Our new list of wide systems with Hipparcos primaries includes 130systems identified here for the first time, including 44 in which the secondarystar has V>15.0. Our census is statistically complete for secondaries withangular separations 20 arcsec < Delta theta < 300 arcsec and apparentmagnitudes V<19.0. Overall, we find that at least 9.5 % of nearby (d<100 pc)Hipparcos stars have distant stellar companions with projected orbitalseparations s > 1,000 AU. We observe that the distribution in orbitalseparations is consistent with Opik's law f(s) ds ~ s^{-1} ds only up toseparation s \approx 3,000 AU, beyond which it follows a more steeplydecreasing power law f(s) ds ~ s^{-l} ds with l=1.6+/-0.1. We also find thatthe luminosity function of the secondaries is significantly different from thatof the single stars field population, showing a relative deficiency inlow-luminosity (8<M_V<14) objects. The observed trends suggest either aformation mechanism biased against low-mass companions, or a disruption overtime of systems with low gravitational binding energy.Comment: 18 pages, to appear in The Astronomical Journa

New Distant Companions to Known Nearby Stars. II. Faint Companions ofHipparcosStars and the Frequency of Wide Binary Systems