3C 84 (NGC 1275) is one of the brightest radio sources in the millimetre radio bands, which led to a plethora of very-long-baseline interferometry (VLBI) observations at numerous frequencies over the years. They reveal a two-sided jet structure, with an expanding but not well-collimated parsec-scale jet, pointing southward. High-resolution millimetre-VLBI observations allow the study and imaging of the jet base on a sub-parsec scale. This could facilitate the investigation of the nature of the jet origin, also in view of the previously detected two-railed jet structure and east-west oriented core region seen with RadioAstron at 22 GHz. We produced VLBI images of this core and inner jet region, observed over the past twenty years at 15, 43, and 86 GHz. We determined the kinematics of the inner jet and ejected features at 43 and 86 GHz and compared their ejection times with radio and γ-ray variability. For the moving jet features, we find an average velocity of β avg app = 0.055 − 0.22c (µ avg = 0.04 − 0.18 mas/yr). From the time-averaged VLBI images at the three frequencies, we measured the transverse jet width along the bulk flow. On the ≤ 1.5 parsec scale, we find a clear trend of the jet width being frequency dependent, with the jet being narrower at higher frequencies. This stratification is discussed in the context of a spine-sheath scenario, and we compare it to other possible interpretations. From quasi-simultaneous observations at 43 and 86 GHz, we obtain spectral index maps, revealing a time-variable orientation of the spectral index gradient due to structural variability of the inner jet.

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