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We present pulse width measurements for a sample of radio pulsars observedwith the MeerKAT telescope as part of the Thousand-Pulsar-Array (TPA) programmein the MeerTime project. For a centre frequency of 1284 MHz, we obtain 762$W_{10}$ measurements across the total bandwidth of 775 MHz, where $W_{10}$ isthe width at the 10% level of the pulse peak. We also measure about 400$W_{10}$ values in each of the four or eight frequency sub-bands. Assuming, thewidth is a function of the rotation period P, this relationship can bedescribed with a power law with power law index $\mu=-0.29\pm 0.03$. However,using orthogonal distance regression, we determine a steeper power law with$\mu=-0.63\pm 0.06$. A density plot of the period-width data reveals such a fitto align well with the contours of highest density. Building on a previouspopulation synthesis model, we obtain population-based estimates of theobliquity of the magnetic axis with respect to the rotation axis for ourpulsars. Investigating the width changes over frequency, we unambiguouslyidentify a group of pulsars that have width broadening at higher frequencies.The measured width changes show a monotonic behaviour with frequency for thewhole TPA pulsar population, whether the pulses are becoming narrower orbroader with increasing frequency. We exclude a sensitivity bias, scatteringand noticeable differences in the pulse component numbers as explanations forthese width changes, and attempt an explanation using a qualitative model offive contributing Gaussian pulse components with flux density spectra thatdepend on their rotational phase.

The Thousand-Pulsar-Array programme on MeerKAT: -- VI. Pulse widths of a large and diverse sample of radio pulsars