  We present the results of near-infrared H-band (1.65 microns) imaging of 19
steep spectrum radio quasars (SSRQ) in the redshift range 0.5 < z < 1.0. This
sample of SSRQs is matched with our previously studied complete sample of 20
flat spectrum radio quasars (FSRQ) with respect to redshift and optical and
radio luminosity. We are able to clearly detect the host galaxy in 10 (53 %)
SSRQs and marginally in 6 (32 %) others, while the host remains unresolved in 3
(16 %) SSRQs. The galaxies hosting the SSRQs are large (average bulge
scale-length R(e) = 9.0+-1.7 kpc) and luminous (average M(H) = -27.2+-1.1).
They are, therefore, about 2 mag more luminous than the typical galaxy
luminosity L* (M*(H) = -25.0+-0.2), and about 1 mag more luminous than the
brightest cluster galaxies (M(H) = -26.3+-0.3). The SSRQ hosts appear to have
similar luminosity to those of the FSRQ hosts (M(H) = -27), and they fall
between the luminosities of lower redshift (M(H) = -26) and higher redshift
(M(H) = -29) radio-loud quasars. The average nucleus-to-galaxy luminosity ratio
of SSRQs (LN/LG = 3.8+-3.2) is much smaller than that found for the FSRQs
(LN/LG = 21+-11), in good agreement with the current unified models. We confirm
for the most luminous SSRQs the trend noted for the FSRQs between the host and
nuclear luminosity. This trend supports the suggestion based on studies of
lower redshift AGN, that there is a minimum host galaxy luminosity which
increases linearly with the quasar luminosity. Finally, FSRQs seem to reside in
richer environments than SSRQs, as evidenced by a larger number of close
companion galaxies.
