We use numerical simulations to model the migration of massive planets at small radii and compare the results with the known properties of `hot Jupiters' (extrasolar planets with semimajor axes a < 0.1 au). For planet masses Mplsini > 0.5MJ, the evidence for any `pile-up' at small radii is weak (statistically insignificant), and although the mass function of hot Jupiters is deficient in high-mass planets as compared to a reference sample located further out, the small sample size precludes definitive conclusions. We suggest that these properties are consistent with disc migration followed by entry into a magnetospheric cavity close to the star. Entry into the cavity results in a slowing of migration, accompanied by a growth in orbital eccentricity. For planet masses in excess of 1 Jupiter mass we find eccentricity growth time-scales of a few ×105yr,suggesting that these planets may often be rapidly destroyed.Eccentricity growth appears to be faster for more massive planets which may explain changes in the planetary mass function at small radii and may also predict a pile-up of lower mass planets, the sample of which is still incomplete.