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Abstract Pulsar timing arrays have found evidence for a low-frequency gravitational-wave background (GWB). Assuming that the GWB is produced by supermassive black hole binaries (SMBHBs), the next gravitational-wave (GW) signals astronomers anticipate are continuous waves (CWs) from single SMBHBs and their associated GWB anisotropy. The prospects for detecting CWs and anisotropy are highly dependent on the astrophysics of SMBHB populations. Thus, information from single sources can break degeneracies in astrophysical models and place much more stringent constraints than the GWB alone. We simulate and evolve SMBHB populations, model their GWs, and calculate their anisotropy and detectability. We investigate how varying components of our semianalytic model, including the galaxy stellar mass function, the SMBH–host galaxy relation (M_BH–M_bulge), and the binary evolution prescription, impact the expected detections. The CW occurrence rate is greatest for few total binaries, high SMBHB masses, large scatter inM_BH–M_bulge, and long hardening times. The occurrence rate depends most on the binary evolution parameters, implying that CWs offer a novel avenue to probe binary evolution. The most detectable CW sources are in the lowest frequency bin for a 16.03 yr PTA, have masses from ∼10⁹to 10¹⁰M_⊙, and are ∼1 Gpc away. The level of anisotropy increases with frequency, with the angular power spectrum over multipole modesℓvarying in low-frequencyC_ℓ>0/C₀from ∼5 × 10⁻³to ∼2 × 10⁻¹, depending on the model; typical values are near current upper limits. Observing this anisotropy would support SMBHB models for the GWB over cosmological models, which tend to be isotropic.