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We had previously reported on a survey for radio transients, used to set anupper limit on the number of orphan gamma-ray burst (GRB) radio afterglows, andthus a lower limit on the typical GRB beaming factor. Here we report radio andoptical follow-up observations of these possible transients, achieving thefirst full characterization of the transient radio sky. We find that only twosource are likely to be real radio transients, an optically obscured radiosupernova (SN) in the nearby galaxy NGC 4216, and a source not associated witha bright host galaxy, which is too radio luminous to be a GRB afterglow. Wespeculate that this may be a flare from a peculiar active galactic nucleus, ora burst from an unusual Galactic compact object. We place an upper limit of 65radio transients above 6 mJy over the entire sky at the 95% confidence level.The implications are as follows. First, we derive a limit on the typicalbeaming of GRBs; we find f_b^{-1} >~ 60, ~5 times higher than our earlierresults. Second, we impose an upper limit on the rate of events that eject >~10^{51} erg in unconfined relativistic ejecta, whether or not accompanied bydetectable emission in wavebands other than the radio. Our estimated rate,<=1000/y/Gpc, is about two orders of magnitude smaller than the rate ofcore-collapse SNe (and type Ib/c events in particular), indicating that only aminority of such events eject significant amounts of relativistic material,which are required by fireball models of long-soft GRBs. Finally, we show thatfuture wider and/or deeper radio variability surveys are expected to detectnumerous orphan radio GRB afterglows. Our survey also illustrates the greatpotential of sensitive surveys with new instruments to revolutionize the studyof nearby SNe (abridged).Comment: Submitted to ApJ. Comments welcom

Radio and Optical Follow‐up Observations of a Uniform Radio Transient Search: Implications for Gamma‐Ray Bursts and Supernovae