We find that bipolar active regions that emerge onto the Sun's surface are part of a smoothly decreasing frequency distribution that spans almost 4 orders of magnitude in flux and 8 orders of magnitude in frequency. Distributions of emergence latitude and dipole orientation narrow from nearly uniform for the smallest observed ephemeral regions (~5 × 1018 Mx) up to narrowly distributed about the mean for the largest active regions (close to 1022 Mx), while the emergence frequency increases smoothly and rapidly with decreasing flux. At the low end of the flux spectrum, the cycle variation in emergence frequency is at most a factor of 1.5, in antiphase with the cycle variation of close to an order of magnitude for the large active regions. We discuss a scenario in which the ephemeral regions with fluxes below ~30 × 1018 Mx have their origin in a turbulent dynamo, largely independent of the global sunspot cycle. Our empirical findings are based on a combination of previously published work on active regions and large ephemeral regions, complemented here with an analysis of the photospheric magnetic field outside active regions, as observed in SOHO/MDI full-disk magnetograms taken from the most recent sunspot minimum in 1996 to about 1 yr after sunspot maximum in 2001. We find that the spectrum of the emerging bipoles with fluxes (6-30) × 1018 Mx can be approximated throughout this period by a fixed exponential distribution with an e-folding scale of (5.3 ± 0.1) × 1018 Mx. We confirm that the ephemeral regions are an important source of flux for the quiet magnetic network, in particular for the smallest scales; the larger scale patterns are dominated by flux dispersing from decaying active regions. As the variation of these two sources is nearly in antiphase, the flux contained in the quiet-Sun network shows little overall variation: the flux spectrum and the total absolute flux for network concentrations with fluxes lesssim20 × 1018 Mx are essentially independent of cycle phase. For network concentrations with fluxes gsim30 × 1018 Mx, mostly found in regions populated substantially by decayed active regions, the network flux distribution approaches an exponential for which the e-folding scale increases with sunspot activity from ~20 × 1018 Mx to ~33 × 1018 Mx, as the total flux in this component varies in phase with the sunspot cycle. A comparison of the flux-emergence rate with the network flux implies an overall mean replacement time for flux in quiet Sun of 8-19 hr.